It's true, F1 does still run 13" rims. But its not for performance. Its simply because that's what the rules say. And the rules have said the exact same thing for over 20 years now.
Not to mention that bringing F1 tires into the mix is almost completely irrelevant. Those tires are built exclusively for those cars, and are designed to work specifically in those conditions. You can't say that about the tires you buy off the shelf. While I don't know why Nascar still runs smaller rims, the same exact thing is true about the tires. If you have a source for nascar tires, by all means have at it. Otherwise, street tire performance is much improved by going with a larger diameter rim. Not to mention the availability of tires and compounds improves significantly. Stick with 15's and you're pretty much stuck with running BFG T/A's in anything wider than 225.
It's not really a question of whether or not you can make a tire for a 15" rim that will perform in spectacular fashion. If you have a Nascar or F1 budget you can pretty much make anything you want as long as it doesn't go against the laws of physics. But for most folks, its a question of what tires you can actually buy for your car and run on the street. And if you look at the street tires available for 15" rims, and you look at the street tires available for 17" and 18" rims, there's really no question about what will perform better.
