It’s important that tired are true and round. Even a little bit out and balancing will become a nightmare.
Absolutely.
Back in the late 70's I purchased a set of Minilites from another Europa owner; partly because they were the genuine article and partly because they came with new Avon 165/60 tyres which were well regarded.
At the time, 60 aspect ratio was super low, though the diameter was smaller than stock.
The performance and grip was fantastic.
As time went by, the car developed a vibration in the rear.
I chased that vibration around for ages - balanced & swapped wheels, checked wheel centering, half-shaft balance, brake drum balance, engine & gearbox mounts . . everything.
It turns out that an 'out of roundness' had been developing.
At the first wheel swap, the problem went away but in the end, they all developed the same out of round issue - some later than others.