Can a vehicle have too much horsepower?

My 65 once had a cammed 451 with ported heads, single plane intake, 850 TQ, 3.91 rear and a mild convertor. The first time I rolled it out, I was thinking this is gonna be fun. Fun turned to "What was I thinking?" when i accelerated out of a left turn lane and promptly swung the back end out. Ended up recovering but it took all 3 lanes to get it straight again and I wasn't even going that fast. I just ran out of tire as the 205/75's were not up to the task. The suspension was nothing special, just 340 torsion bars and Koni's. Rear was stock "S" 5 leaf. No frame connectors, just a big heavy motor in a car chassis designed for a 225. The slightest gas underway wound up the convertor and broke the tires free. FFWD a few years and I'm back to an LA or a slant, weight is under control (although the 451 was not much heavier than the LA) and the power is more in line with what the chassis is set up for. Safety first. fun second. At least I started with disk brakes.....