Have you ever even seen the underside of a factory panel for these games? They're routed out where the base sits.
Sorry, but you're simply wrong that there are 4" sticks in these games. Maybe if you're using a recut panel you'd need 4" to get the clearance.
I don't know what the point is of arguing it, seems rather silly, but here's a shot of my TMNT control panel for posterity...and they sit 1" above. This is an original CP, as are others I've worked on recessed like this. The sticks I pulled out were 3.5", sticks that went in were as well.

Can't say I've ever seen purple 4" sticks anyway, yellow maybe...blue, I'm not sure.
P.S. Yeah she's dusty...she gets no love anymore and must hate my pins.