I feel that the music/song dictates the sound of the drums, and given that we normally have one kit to play for a whole gig, we have to pick the sizes and tunings that will work well for everything.
For almost any derivation of 'rock', I think a 5x13 snare is borderline. It certainly can work, but is going to be less-suited to as many songs as a 6.5x14 that can be changed from crack to warmth in the moments between songs, or just left 'in the middle' to cover everything.
You wouldn't play a jazz gig with a Bonham kit, and you wouldn't play Led Zep with a bop kit. But with a 22/13/16, you can reasonably cover both. Sometimes the norm ends up being the most versatile on a given night.
Drums make a certain range of sounds for their size, which is why different sizes are available. If tuning was the only aspect to a drum's sound, drum companies could make a 22" kick, 14" tom and 13" snare, and call it a day. Yamaha could make a single 23" timp to cover all the ranges... it tunes high and low, right? Orchestras & schools could purchase 3 or 4 or 5 as needed, and they'd all be the same price - cool! Why pay extra for those pesky 32" timps?? For that matter, they could just make 20" timps, and save space, too!
I understand the sentiment of the remark "Do you want to sound like the rest or sound like the best?" But the fact is, if you want to sound like a pro, you do what the pros do... and that's to use the appropriate sized drum for the gig at hand.
That's why pros have multiple snares and kits. While it may not be practical or affordable for most of us to have 30 snares on hand, it's important to have a few. Smallish, deepish, metal and wood: 5x13 (steel and wood) and 6.5x14 (brass and wood.) Those four snares could do a lot for one drummer.
Bermuda