Many repair shops will replace your screen and battery for you. It’s pretty standard. You don’t need a Fair phone to do that.
That's true-ish. The repairability of phones varies a lot, with some even having batteries glued into the model.
If you're just considering repairability, a fairphone is almost certainly one of your best options. But like you point out, that doesn't mean all other options can't be repaired at all.
But for Fairphone repairs you don't even need a repair shop.
A friend of mine had a broken finger print reader (a few cents online), he couldn't find any repair shop who wanted to repair it (probably because the display would have to removed).