Depends if you want to support phones that exist today, rather that future phones that will support Vulkan.

Also, Vulkan doesn't exist yet, so everything about it is a prediction. Maybe BC/ETC/PVRTC support will be optional...

I think you mean ASTC as the common format, not BC. Hopefully everyone will settle on ASTC in a few years but we're not there yet and there's a lot of legacy devices.

The problem is not API support or GPU support. The problem is that all these formats are patented.

PVRTC1/2 is awesome, but it is patented and exclusive to PowerVR GPUs.

BC1-BC3 is okeish, but is patented but licensed in the Desktop world.

BC4-BC7 is cool, but is patented but licensed in the Desktop world.

ETC is not good, but it's free and "what we've got on mobile".

ATSC is really good (possibly the best) and royalty free, but it is very recent, adoption is far from being widespread yet.

Btw. Metal does not currently support BC on mobile. Patents. I suggest you look at the support chart (page 87).

"since Vulkan and Metal support BC compression and is used for mobile too, is it the end of multiple compression for one unified compression ?"

I'm not sure if the OP meant BC or ASTC, but metal support for both is device-dependent: https://developer.apple.com/library/ios/documentation/Miscellaneous/Conceptual/MetalProgrammingGuide/MetalFeatureSetTables/MetalFeatureSetTables.html#//apple_ref/doc/uid/TP40014221-CH13-SW1

If there is going to be a unified compression (across phones and desktop) it will be ASTC, not BC, but you'll have to wait a good few years before you can assume support.