I don't know, man. I know tons of great IPF/USAPL squatters who use an oly style shoe whether it's the Adidas of a Polish/Russian shoe. The reality of things is Oly lifters do tons of squatting. I don't really agree with that statement. I think they are built for squatting.
The one thing I would say is I rarely box squat because I am one of those guys who squats a lot more to a box than free, but I really get no carry over. It was frustrating, but when I finally just accepted this was when I switched shoes.
Now, if I do a cycle of box squats (about 2X per year), I do them in my Chucks. They feel terrible in my Adidas.
It's kind of like most things in PL from a gear standpoint. You need to use what works for you. Lately, I have been doing a lot of fronts and high bars (free) because I am trying to bring my convo pull up and feel strongly there is a correlation. There's no way I would do these in my Chucks. For me, it feels like shit.
A long time ago I was told by someone much more talented than I that in terms of achieving depth you can do two things. Squat deeper or elevate the heel. I think having an elevated heel helps when you have to break parallel and you squat RAW or in gear that has less stopping power.
It's kinda like ramps for a sumo puller (which the IPF made illegal which is ridiculous IMO). Some lifters do very well in them. Some are totally thrown off.
You just have to try it and see.