Toyota is a Japanese manufacturer, selling cars worldwide. They have several ‘boring’ cars in their line – up, but their selling point is that they’re generally accepted worldwide as the most reliable car manufacturer in the world, along with their luxury brand Lexus.
The American ‘performance’ car market is unique – Dodge, Chevrolet & Ford make cars for the home market that are pretty much 100% restricted to the US in their appeal – no – one else anywhere else in the world wants them, or buys them in any quantity. They are built with large engines & are designed as ‘cruisers’ rather than sports cars – they are large & overweight, and as you say, that’s the basis for American circuit racing such as the NASCAR series, which again has no following outside the US.
In the rest of the world, true sports cars are bought for their technology: power per litre, handling, suspension, weight saving, etc. which is why cars like the Subaru Impreza sell worldwide – the US doesn’t appreciate the technology & still want a big V-8 engine, regardless of it’s ability to get traction or to go round corners. They don’t ‘excite’ people in Europe, Asia or Australia, as motorsport tends to involve rallying, or complex circuits.
The US still has very cheap fuel, due to the government not wishing to upset the people, and the car buyers have historically been VERY patriotic – up until very recently, you wouldn’t see an ‘import’ anywhere, so the home built cars never needed to compete. This has made a unique scenario where things like Indycar & NASCAR racing are isolated to the US, and foreign makers don’t tend to bother with getting involved.
Take a look at the Worldwide motorsports series – Formula 1, The Word Rally Championship, World Superbikes, Moto GP etc., where the US makers don’t generally have anything that will compete.
On four wheels, Toyota have been involved with Formula 1 for years, and dominated the WRC championship for several years.

If you want a super fast and high powered Toyota, it ain’t gonna happen. However Lexus does make the IS-F with a V8 and over 400 horsepower, not sure what the price is. Nissan just unleashed the GTR, AWD, 480HP for $75000 and it will smoke any American made car including the Ford GT and Corvette Z06. Hyundai has the new Genesis sedan with 4.6L V8 putting out 375 HP with all the luxury you could imagine for $42000 that beats all the cars you named in handling/performance (except Viper/Vette). I’m not sure what Honda’s doing S2000 is old and NSX is supposed to be replaced soon. Mazda’s RX-8 is okay, but their Speed3 and Speed6 were better cars with more power.

The thing you have to remember is that Japanese companies never needed to make a V8 since their V6’s were always as powerful and more fuel efficient then American engines. In Europe they just put a turbo or supercharger on all their 4/5/6 cylinder engines for extra power.