Yup, most of these factory cars coming out at those power levels are really not properly setup to have that kind of power. You look at stuff with that much power and it's already in the arena of need a 6-point roll bar in it.
I daily drove my '06 until it was in the 930 hp range. The way I tuned it was so that it was totally tame in the first 50% of the throttle. You'd never even know it had the kind of power it did if you drove it like a sane person. I bring the power in harder from 50 - 75% throttle. No kill mode power, but you know it's coming. Over 75% throttle was straight kill mode. If you didn't know that it was there, the back end and front end would swap sides in a heart beat on street tires. The '06 is completely useless as a street truck now. Big turbo, 2 kits, caged, 4 drag radials, 1551 hp.....it's just stupid. I'll still drive it on the street, like to and from the track for a "street" race, but that's it. Otherwise it's a trailer queen now.
Now, the '88 will put down 890 hp at the tires, but I turn it WAY down on the street. On the ET Streets I'll give it 14 psi on pump gas and that is about the limits of usefulness. On the track and slicks I'll turn it up to 22 psi. It's in the 600's at 14 psi.
I've had guys tell me they want 700+ in their truck and as soon as you ask them have they ever driven something with that kind of power it's always the same thing, "Well, my buddy has this bad a$$ car..........", yeah okay..... Take 'em for a ride in the truck and I'll find a spot where the road is crowned pretty good and bring it up to around 20 psi. Launch in 4wd and it'll slide 2 feet sideways before it moves forward an inch. There's usually finger marks in the door handle and console. Their power expectation suddenly goes down to the 400 - 500 range. lol
For me, 600 - 650 puts me in the range of a 10 second car on radials. That's where I like a street car. It's too much for street tires, but that comes with having enough experience to know when you're pushing the limits. That power normally won't hook from a dig on pavement, but concrete and radials is a whole different story.