Its a problem, because you can only buy tyre sizes that are available.
There's a good range of tyre sizes for 16" wheels, but they're expensive.
And tyres for 15" wheels are cheaper, but that's at least partly because people usually buy larger wheels for performance, and smaller wheels for cheapness, so there isn't the range of good tyres.
15" wheels and low profile 205s, ideally 205/45s or 205/40s, would be good on the track. It'd reduce wheel weight. It'd reduce tyre diameter which would lower the car and improve handling. And it'd lower the gearing a bit and improve acceleration. You don't need as high a top speed. But you can't get road tyres that size. Its just not what anyone needs on the road.
If its just for the track, what about a set of hardish racing tyres on 15x7 wheels? There are a couple of different one-make classes that have tyres about the right size. And racing tyres are fun.