I reckon most BIAB brewers squeeze the bag. Has absolutely no negative effects that I, or many others, can detect. A few authors claimed it added astringency, but that's pretty much considered to be a myth nowadays. Much like the one about BIAB giving lower efficiency. lol Most software profiles when set to BIAB for the mash actually assume you are squeezing the bag in the grain absorbency calculation I believe, so you can end up coming up short on your boil volume if you don't too, possibly.
Personally, I go for a decent dough in (don't just dump the grain in, give it a quick stir, then leave it), one or 2 good stirs during the mash, then a good mash out at the end instead of sparging. Raise the bag, give it a good squeeze, then rest it on a cooling rack over the boiler to let it drip for a bit whilst I heat the wort up. Works for me anyway, just have to make sure to keep stirring the wort whilst heating to the boil as been an eBIAB rig I have an element in there that will end up with wort scorching onto it if I don't...
The only difference you MAY notice with squeezing is in wort clarity. Doesn't impact flavour though. Just weigh up adding more water and a bit more grain and getting slightly less haze, or giving it a squeeze, not much in it either way to be honest, unless you're pressed for space in your vessel that is, then squeezing is the only choice really.