I always do the OS installs through iTunes so it pretty much gets wiped every time.

Maybe that's the issue - I don't do OS updates on iOS devices, so my 5s is still on iOS 7.1 - and it's still blazing fast after 18 months of use. My suspicion is that the iOSes getting slower with every release is a planned obsolescence strategy.

I don't buy it. Each revision of the OS adds functionality and expands the code base, that's plenty enough to explain the issue. Long term, progressively bogging down the OS deliberately will just make it look unnecessarily slower compared to Android. That's a much bigger risk than any possible effect getting people to upgrade.

Also there are ways to disable some of the newer features and reclaim some responsiveness, such as General->Accessibility->Reduce Motion.

I was thinking it may not be an official agenda ("plans for Q4: let's make iOS 10% slower"), but instead, the higher ups don't actively fight the general performance athrophy.