Correct me if I'm wrong, but I do believe that it's wrong to say that PS2 and PSX's chip instruction sets were different.

PSX, PS2, and PS4 use the same instruction set and PS4 is actually stepping back to the conventional instruction set that has been around for a decade or so.

PS3 uses a different instruction set due to the cell processor and how they used the processor.

PSX, PS2, and PS4 use CPUs/GPUs specifically designated to their function so they know what they are doing and their processing power and all that...

PS3 uses one huge multi-core thing that is just there and all its processing power is always in flux and always changing to meet it's current demands.

So to emulate PSX, PS2, and PS4 on PS3 they need to write an emulator that handles all those instructions and assigning them to the processor correctly... which I imagine is pretty hard.

Reversing it to emulating PS3 on PSX, PS2, and PS4 requires that coding that does all that be removed and the piped to the correct processor... again... I imagine that is a fairly hard thing to do.

Either way you are looking at a reduction of efficiency and possibly a huge overhead that wasn't previously there which can cause massive amounts of problems with running the game in a playable way even without considering how many times the emulator makes a mistake and doesn't remove/put in the proper code which causes pretty bad problems too that make certain games unplayable on their own.

And while the consoles tend to be of greater ability than their previous generation it just isn't enough to overcome those problems. Or it just ins't worth it to developers, largely because they don't understand that every "wireless" and internet thing they put out makes their stuff less attractive to the audience they get most of their money from currently... Shooter gamers. Having streaming games do not work for Shooters because they introduce just that much more lag and lag is the bane of Shooter fans. Also because emulators are not something you can charge for...where as you can charge fir new versions of the same thing over and over again.

Correct me if I'm wrong, but I do believe that it's wrong to say that PS2 and PSX's chip instruction sets were different.
PSX, PS2, and PS4 use the same instruction set and PS4 is actually stepping back to the conventional instruction set that has been around for a decade or so.
PS3 uses a different instruction set due to the cell processor and how they used the processor.

The PS1 and PS2 CPUs have the same core instruction set, although the PS2 has several instruction set extensions as well. Furthermore, the PS1's geometry transform coprocessor is totally incompatible with the PS2's vector units; since coprocessor instructions are mixed into the code stream, this means that almost all PS1 code won't run on the PS2 CPU. So while their instruction sets are related, they aren't the same.

The PS4's CPU is a completely different instruction set from other Playstations - the PS1 and PS2 used MIPS CPUs, the PS3 CPU uses Power Architecture, and the PS4 uses an x64 CPU.

The main reason Sony broke compatibility is believed to be purely business by some. They have stated on multiple occasions that they are trying to make their PS1 and 2 games available through the Playstation Network, but now with the PS4 out and PS3 nearing its end they can put PS3 on the PSN. If they did that, they could make you pay to buy them all over again. They claimed they were going to put a voucher program or something similar in place where you could send in your games to get a voucher so you could download them without paying again, but that never happened.

When they dropped PS2 compatibility in the PS3, they claimed it was to save money, but some believe it was because the PS2 was still selling and PS3s playing those games was hurting the sales they could make on the PS2.

Breaking backwards compatibility also has benefits too. At least that is what I'm told ;).

There are always pros and cons, but I will be worried when the cons outweigh the pros and a company still goes through with it.

I've not read all the Xbox One conspiracy theories yet so I can't comment on them, but I know they are going to be both funny and ridiculous just like the PS3 and PS4 theories were.

Also I've heard rumors you can rip open the hardware and play different cartridge games on a Sega Genesis.

Not quite.

The Genesis is backwards-compatible with the Master System, but it requires an adapter (the Power Base Convertor), partly because the cartridge connectors don't match. However 3 or 4 Master System games don't work on the Genesis.

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In more detail:

The Master System uses a 3.58 MHz Z80 CPU with 8 KB of RAM, a 4-channel programmable sound generator, and a graphics chip based on the TMS9918 (also used in the ColecoVision, MSX, and TI 99/4A among others) with an added graphics mode - the added graphics mode is the the standard, used in almost all Master System games. (Later models of the Master System added a primitive FM synth audio chip as well.)

The Genesis uses a 7.67 MHz 68000 main CPU with 64 KB of RAM, a 3.58 MHz Z80 secondary CPU with its own 8 KB of RAM (primarily used in Genesis games to control the audio hardware), the same 4-channel PSG, an FM synth audio chip (not compatible with the one used in later Master Systems), and a graphics chip based on the one used in the Master System (it featured a new graphics mode used by Genesis games, but removed the original 4 TMS9918 graphics modes). Additionally, the controllers use the same communication protocol as the Master System controllers. The cartridge connector also features a pin that can carry a signal that disables the main CPU.

The Power Base Converter has slots for Master System cartridges and cards, and when one is plugged in it uses the main CPU disable signal to allow the Z80 full control over the system. However, a small handful of Master System games use one of the 4 original TMS9918 graphics modes (rather than mode 4, the Master System mode) and thus will not run on the Genesis.

The convertor was made a separate accessory rather than being integrated into the console because the Master System frankly did not sell very well in most territories, and out-of-the-box backwards compatibility is only a strong selling point when following up a successful system.

They claimed they were going to put a voucher program or something similar in place where you could send in your games to get a voucher so you could download them without paying again, but that never happened.

When they dropped PS2 compatibility in the PS3, they claimed it was to save money, but some believe it was because the PS2 was still selling and PS3s playing those games was hurting the sales they could make on the PS2.

Do you have a reference/link to this voucher program rather than just making a claim? In fact Sony has run two such programs that were very specific, one that was for the PSP and the latest which was the PS3->PS4 upgrade vouchers for launch window titles.

Regarding compatibility Sony cut the emotion engine from the original PS3 fabrication in order to lower cost which is what consumers demanded over backwards compatibility. Not to mention your statement makes absolutely no sense because Sony makes money on software licensing and not hardware sales, so it is actually in their best interest to be backwards compatible and sell PS2 games to PS3 owners.

Do you have a reference/link to this voucher program rather than just making a claim?

I don't have the specifics to it, just that it was talked about when gamers wanted to know what they were going to do with their PS2 games now because most didn't want to go buy a PS2. I don't think it ever came about.

Not to mention your statement makes absolutely no sense because Sony makes money on software licensing and not hardware sales, so it is actually in their best interest to be backwards compatible and sell PS2 games to PS3 owners.

You need to read it again. I never said I thought they did, but that some do as it was addressed by several gaming magazines. There are conspiracies online for every system every time a system was changed.

Though, I don't know about the lower cost by removing PS2 support. I paid the $600 to buy the PS3 when they first came out, a couple years back my PS3 quit working, but because my son couldn't wait for it to be repaired we bought a new one (without PS2 support) and it was still over $550, not much of a savings in my eye. I, personally would have rather had the PS2 support and paid more instead of now where I have my PS2 collection and no way to play them and no way to sell them. At the time I bought the PS3 with no PS2 support companies like GameStop no longer bought used PS2 games and I still have several I liked playing.

low level optimalisations are bad.

no offence but you should go back to school or start over.