I use my phone all the time, so like many were happy to pay for a better experience. The smoothness of the UI and particularly browsing is dramatically better to my eyes with the higher refresh rate screens. I have a 13 Mini here too and it feels like a slideshow in comparison. I think different people are affected more or less by it but I’m a long time gamer and it bothers me so I’d pay more for that (as I did for the 16 Pro).
I haven’t noticed any issues with battery, quite the opposite to be honest.
I find that very hard to believe for a phone UI, 60Hz is certainly not 30Hz, which is what I'd consider a reasonable comparison to a slideshow, not 60.
IOS has always ran nicely on pretty much every iPhone - bar when you push your luck years and years later, trying to run a modern IOS version from a brand new phone on a fairly older model.
Nagivating a phone is hardly comparable to say playing competitive FPS, where you'd clearly benefit/notice 120/144/165Hz and above.
Granted it will
obviously be smoother than 60, there's no denying that, but to compare 60Hz to a slideshow is a stretch.
It just seems like another fad to sell phones, just like the OTT branded 'gamer' scene tax priced stuff in the PC/console scene, that they clearly market for kids to fall into the trap of.
Either way, each to their own

If you like it and feel that it really is
that much of a jump, and want to pay the extra, fair play to you
