I have an iPhone 6S - I'd say OS updates do slow the phone down, but they also tend to be really buggy and generally rubbish for a while. I think it's probably more bad engineering and software quality than anything nefarious.
[1] http://money.cnn.com/2017/12/21/technology/apple-slows-down-...
The said that as the battery degrades, they limit CPU spikiness that can abruptly kill the device even with a non-trivial amount of juice left.
That's not nearly the same as "slowing down the phone with every upgrade".
Often people have reported better performance after an OS upgrade, although obviously results may vary, and subjective impressions are always, well, subjective.