Are their any video games like this?

I don't get any of this, honestly.  I'm lost on the logic behind any of these points.

Yes.  Why would games made in the 2020s only have cars from 2000 and earlier?

This is a gross oversimplification of motorsport and car performance.  Yes, a modern Mustang will outperform a Mustang from 1967.  However, a 2023 Honda Civic won't outperform a 1976 Ferrari 312 T2.  A modern Hyundai Elantra won't outperform a 1993 McLaren F1.  (Despite the name, the McLaren F1 wasn't a F1 car.)  Racing games featuring a variety of cars often won't have 1960s cars competing against 2020s, so which performs better doesn't really matter, and racing games typically have upgrading so you don't have to race the cars stock.  Modern racing games like Forza Motorsport or Gran Turismo have a broad range of cars from all categories and time periods, not simply for their performance but because they are for people that love cars.

What good reason is for modern cars to not be in modern games outside of racing?

Specific examples of modern games with modern cars, besides racing, are hard for me to produce, however, not because they don't exist but because I don't play all games.  I do a lot of racing, but otherwise not a lot that takes place in a modern Earth setting.  Grand Theft Auto uses modern cars, but for licensing reasons they aren't direct knockoffs but rather have changes and different names, but they're clearly inspired by modern real cars.  Using such cars would only make sense in games set in 1) the real world and 2) in our time.  They're often in fictional worlds, in space, in different historical periods, in post-apocalyptic Earth, et cetera.