There are still some 4:3 screens kicking around I'm sure, but its been nearly impossible to buy one off-the-shelf for ages, except for a handful of PC monitors marketed mainly to corporate environments. Back in the day, the question was "how do I design for 4:3 and 16:9?" and now its "How do I design for 16:9 and 21:9?". I think the difference is that 16:9 was clearly going to be where things moved to, but it doesn't seem so clear for 21:9. Oh, unless you're also dealing with iPads, or the myriad other devices as well (though, then you get a pass on 21:9, so far)
But the approach is the same -- either you design such that the extra information isn't beneficial, or you hide it. When you take the design approach, what you're really doing is letter-boxing the design process itself -- you can't place essential information outside the safe area, and you have to think about whether even revealing information sooner to players with different aspect ratios gives them an advantage. Letter-boxing the player's screen is essentially a design-choice to simply ignore these same questions.
Now, something to keep in mind is that this matters most for competitive scenarios -- that's when one player gets a direct advantage over another and fairness is the primary objective. In single-player, non-competitive scenarios, the questions can still matter, but the effect is different; there, your objective is more concerned with ensuring that the pace of progress and level of exploration is not affected. Even in single-player games, though, there can be competitive elements like leaderboards, speed-runs, etc. What's important will depend on what kind of game you're making.
I tend to think, myself, that the best way to approach this in this day and age is to employ a dynamic camera that adapts to a design-safe area that's independent of any particular aspect ratio, and which itself may not match any popular aspect ratio one finds in the real world. That approach doesn't really work for pixel-perfect, sprite-based 2D games, but is a very good approach anywhere that the pixels aren't crucial to the design or aesthetics.
You also have to address on-screen UI in a flexible way -- not only might it change how things are obscured as aspect ratio shifts, but you might also be inclined to deliver different UI properties to tablet users, PC users, and console users anyways. Most serious developers should already have moved to that way of thinking if its important to where they deliver their games.