Not really, and definitely not with more modern ones. I have an iPhone 11 from 2019. It was released with iOS 13. It is now running iOS 16.1.1. It is as snappy as the day I bought it. I'm considering a phone upgrade, but that's because of the improved camera, not performance (or even battery life).
My old iPhone 8 (2017) is still getting updates, and now is moderately pokey with nontrivial apps, but the OS is fine. And I get it with regards to apps, as the perf and battery improvements between the A11 and the A13 chips was pretty significant.