Engine, pump, oil reservoir, motor, valving, etc. This equates to a fair bit more weight than you may want. Cost, too. Yes, you'd have very fine control over the speed, and yes, it'd be torquey as hell (I regularly use an old Bolens hydro for moving my boat and utility trailers around, and it never breaks a sweat.), I don't think I'd go that way. It would have the power and weight to seriously bulldoze anything your son pointed it at. Ouch!
I started building a kart for my kids a couple years ago (they're now 7 and 9 with no driving experience) and I went with a centrifugal clutch, and jackshaft setup. I can regear for speed as they grow. Right now I've got it up somewhere around 14:1. Controllably slow, and more than enough stones to haul my adult rearend around. I have no worries about roasting that clutch anytime soon. Just for the record, it's a heavy-arse frame (overbuilt it my first time out) and while slow, I mash the throttle and it'll spin the wheels on varying surfaces.
If you build it, it'll work, it'll be cool, and I'll wanna see it. I just don't think you really want to.
Good luck! Cheers- Chris