I wouldn't say that they don't rely too much on engineering as much as they only try to find ways to make an existing design work rather than tackling its shortcomings. Plus while a lot of American sports cars can generate impressive numbers (horsepower, torque, acceleration, handling, etc.), it usually does so in a less refined manner compared to their overseas competitors. Also, I wouldn't say that weight rarely plays a role for that reason, seeing how only the Viper has a V-10 and no American V-12s are in production sports cars. It's just that large-capacity, low-revving American V-8s have torque smothered all across the rev range that it can get a lot of weight moving off the line pretty easily.
While it's less of an example of that philosophy, the Z06 still displayed such goals, though they did a much better at making dated technology still work quite well. Rather than ditching pushrods for overhead cams, GM stuck with the engine design and applied some modern technology to it and made the LS7. It doesn't make any statements when it comes to hp/liter, but regardless, it's a gem, and it pulls really hard at any rpm and gets quite respectable gas mileage, so it's hard to find fault in the engine. The rear leafspring suspension is pretty ridiculous, but they tuned it really well, as the Nurburgring results speak for themselves. But the use of various materials (carbon-fiber, magnesium, etc.) in key areas was definitely a great idea.
Other cars don't quite pull the job off as gracefully. Retro looks aside, the Mustang was a big let-down not just because it came with a solid rear axle, but also because it found its way to the GT500 whereas the previous SVT Cobra at least had an IRS. Yes, there were measures taken during suspension tuning to make it handle as well as it could rather than just directly carrying over the suspension itself from the standard models, but the fact of the matter is that it is inferior to an IRS, and Ford's attempts to cover up the fact that it was done for cost purposes (since they still wanted the base Mustang V-6 to start at below $20k) with excuses that no publication has bought is just lame. And now they are offering even more powerful versions, like the GT500KR and the Super Snake variations, all with more hp and torque (great if you feel like burning rubber from a 60 mph roll) but still the same archaic rear suspension.
The recent muscle car offerings from Chrysler (300, Magnum, Charger) are all decent, though the handling aspect (not that it is fantastic) is attributed to their previous partnership with Daimler-AG, seeing how their suspensions and 5-speed automatic transmissions were all sourced from the previous-generation Mercedes E-Class. The downside is that these cars are HUGE, though the demographics that they were targeting are looking for cars like these. And the V-8s aside, the Viper is as unrefined as cars can get, though that is part of the car's charm. Let's not forget how the car started out, with its engine being an 8.0-liter truck V-10 lightly modified by Lamborghini. Personally, I still think the original 1997 Viper GTS was the best looking of all, but the 2008 Viper SRT-10 is actually quite decent with its updated powertrain, as it now has a respectable hp/liter power output. Perhaps the current Viper is the best example of the American way of generating numbers while lacking finesse. It does 0-60 mph in 3.5 seconds, tops out at over 200 mph, pulls over 1.0 g on the skidpad, but it's so unrefined. But to some people, particular objective numbers are more important than subjective feelings.
Personally, I think the best effort at a proper American supercar is the Saleen S7. It definitely looks the part, with its mid-engined/rear-wheel drive setup and carbon-fiber body, plus it always had some styling elements of the McLaren F1, in my eyes... not that they looked alike, but are definitely a few similarities. But beneath the skin is where the car failed. Since Saleen doesn't build engines, he had to outsource, but there aren't really any good supercar-caliber engines worth of being world-class. He ended up getting a 7.0-liter NASCAR V-8 and worked his magic to it, though the engine is still far from being a supercar engine, despite the numbers. It's a relatively low-tech car overall once you go beneath the surface. And the fast 0-60 mph time of 3.3 seconds was mostly attributed to its gearing, so 60 could be hit in first gear, though 0-100 mph was noticeably slower than other supercars with slower 0-60 times, showing the weakness of such a motor in the supercar arena. Saleen eventually made the S7 Twin-Turbo with 750 hp... an answer to a question that wasn't asked. More power is welcome, though it was never really a problem. It handled well, but only because the suspensions were ridiculously stiff due to the chassis tuning, while its competitors had better chassis tuning and more generous suspension tuning that let them be cars that could be comfortably daily-driven. If you've ever seen an S7 in person, you'll realize exactly how low these things are and how difficult they must be to drive up even a standard driveway.
Before the U.S. can make a truly world-class kick-ass supercar, they need to put emphasis on a few things. Chassis tuning is a big deal, since it will also play a role in suspension tuning. Of course Americans would never in a million years want to outsource engines for a proper supercar, but big V-8s won't cut it. A proper supercar needs to have great sound and perform more and more excitingly as the rpms climb. Also, it should be civilized and the power delivery should never be too much at a given moment. For example, the V-8 in the Ferrari F430 is perfect and will get you moving at any speed going straight, left, right, wherever in a rather linear but exciting fashion. A typical American V-8 will give you torque right away, though depending on the application, traction could be an issue, especially during a lot of throttle usage in the corners. Also, R&D needs to be done in either a proper high-performance V-10 or V-12 engine with modern technology (DOHC, VVT, direct injection, etc.) with efficiency in mind. Yes, there are American V-8s that put out north of 400 hp, but they're all massive motors, whereas the Japanese and the Europeans can do that with less than 4.0 liters and are MUCH more fun to drive. "FUN" is the keyword that Americans need to focus on, not "easy."