That's near enough to true for anyone not operating at "web scale".
FAANG/BAT engineers need to care. My systems with 10s or 100s of thousands of users (or, you know, a few thousand users tops) are without doubt going to be re-written (probably several times) well before I have to worry about having so many UUIDs in the wild that this becomes a reasonable thing to worry about.
For me, at the scale of systems I run (or will conceivably run in the medium term future), I think the simplicity/understandability of code that uses native language UUID functions is "the right thing". Whoever does the next big rewrite to support a few million MAU will be thankful they don't have to work out WTF I was thinking when I decided to roll my own random access tokens.