I raced Karts & had a KT100. For those watching, the KT100 was introduced by Yamaha in the early 70's and is a specific kart racing engine still used today in many places.
Even though the kart it came on (The RC100) was a complete failure because of it's "dead frame", the engine became part of numerous racing circuits.
KT100's are finicky turds but are fun to drive. Common racing RPM's can get well above 10,000 and mine was around 12. Temps on the engine get to 400+ degrees but watch it, if they go much further, it'll blow. Make absolutely sure your temp gauge in the onboard computer works.
Yes, on start they usually go way up in idle for the first little bit but then come back down. If it's way up there for MINUTES, there is something wrong. Clean that carb & check things. Don't worry about the high rev too much as the gas and oil are already lubing the thing, it's a 2 stroke.
There is no float in the carb, could be a vacuum leak, all kinds of things.
Does it perform just fine?
Keep in mind, racing one of these things requires maintenance. Rebuilds during the season are common. Start of season, fresh rebuild. Half way through, piston rings, possibly a piston & head gasket. Find the rule book on this class because once the engine has been punched out so many times, it'll become illegal to race & you'll need a new cylinder. (or can as they call it)
If you want the fastest KT there is, send it to Woltjer, and you're gonna pay for it... but she'll come back quite fast.
Racing notes:
It looks like you're in the "can" class. Probably 3 or 4 hole can (muffler, 3 or 4 holes) That'll be fun. Make sure the thing is bolted on good. Those can's love to come off.
The clutch, commonly the Horstman HDC is used. 1, 2 or 3 Disc dry clutch. Maintain that thing, it's a 300 dollar clutch. In specific, that inner thrust ring (the little ring between the clutch and the engine... lube it every time.)
Tire pressure & tires. I know you said you got new ones... but in the racing world: New OLD tires do not work for racing. If the tires are old, you're gonna spin out, period. If you have the means, buy new tires. Tires are everything and slides in corners=loss of speed, you're supposed to stick. Tire pressures on cold days, start at 14 up front, 15 in the rear. HOt days, go 11 up front, 12 ish in the rear.
Chains: Commonly a 219 chain is used. Get a spare. You WILL break one. Buy a chain breaker too.
Frame: Look down the rear rails, see if they're straight. If the left side is bent up a bit, get it fixed because it'll cause left turns to fail. It also means it's been in the air at one point. (very likely)
I see a chain guard there, good! Make sure it stays there. When one of these comes off or breaks, pray it doesn't hit you.
The carb: That T-Handle thingy. Turn it in all the way, then out 1 to 1.5 turn to start. After a minute & warm up (maybe half track), turn it out a little more. Play with that.
Alignment: Start at 1 degree toe out & go from there.