Have you read a lawn mower racing rule book (US or ARMA)? Only mower engines are allowed in mower racing. I've never seen a shifter cart I.E. 125 to 250 cc two stroke engine on a mower. However, the Honda GX390 is allowed (horizontal shaft- easier for some to build with).
Plus, I would rather deal with the 1 or 2 wires of a lawn mower engine versus the CDI/stator/wiring harness of a shifter cart. Also, shifter carts use radiators, which have scalding HOT water flowing through them (also not allowed in mower racing).