I have said this before, wire wheels are great flexible flywheels. There is heaps of pics around and you can see the wheel flexing, far more on the bigger dia sedan wheels.
Wheel dia came down on both road cars and racing cars and tyres got wider. Full size passenger cars went from 16 down to 13"and 14" by the early 60s Then started to go up again from the late 70s to the stupid 18 19 20 21" sizes around now.
Most racing categories have either made it or followed it. But F1 has had 13" wheels for decades,, oh and Nascar still use 15" steel flywheels. Though it seems they are a little lighter now.
For a racing car and maybe small capacity Sports Car probably 15" is the go. And probably a 25" tyre. Bigger sports cars and many tin top categories have seldom got bigger than a 27" 18" As a Sports Sedan runner I started off with around 21" high13" rims and tyres, growing to rears at least 23".then went to 15" and later to 16" as 'fashions' changed, and as brakes got bigger. My car eneded up with 13" rotors inside 16" rims. Brakes were in effect GpA Commodore. Now most use 18" rims with it seems some with 14" rotors as do the Supercars. Though the tyres used are generally Sports Car tyres [on Sports Sedans]
With racing cars most have used 13" since the60s, some 5000s used 15". Unsure of the S5000s though I suspect they too are 15".
F1s though going to a bigger dia rim will have to build cars with suspensions!! Making them use tyres for one race too would be a very good idea. Not 7 lap tyres!