You might, might, get some flex with 1/2" ply, especially with 3" wide, and if you mount a controller in the middle of the panel. But you're only thinking 1" deep, which might have enough support. OTOH, you can add 1/2" or 3/4" square cross supports later if needed, if you have space.
OTOH2, If you're putting a 1/4" plexi on top, that might stop/reduce flex, add enough support to route the wood for joysticks if you bolt to the plexi, and help fit standard 3/4" T-molding. (But ply is still hard to slot cut for the T-molding, and the plexi isn't weightless.)
Sorry, I'm doing a lot of devil advocating.