Of all the bikes, I've had, the most susceptible to tyres have been my triples and my Commando.
My first 3CE, back in the very late 70's early 80's when I was almost 11 stone wet through, would go into a tank slapper at 120-125 all the time, until I had enough money to get rid of the worn TT100's and fit Red Arrows (remember them?) they it was fine, or so I thought; but like all triangular tyres, they wore to a flattened round shape, and then the tank slappers came back!
Rounder profile tyres like Phantoms and road runners were much better though.
I think back then a lot of us bought new tyres and thought we'd cured the wobbles, until they wore (I can remember fitting red arrows to my Z1, and marvelling at the transformation, not for long though, roadrunners cured it completely)
Even worn out TT100's were fine on my 3CE with a pillion though, stable as a rock flat in top, so was there some geometry or harmonics at play too??
I would agree with other posters, worn tyres, wheel alignment, but also wheel balance; my 3CE was on wire wheels and they always balanced up fine (old school with plumbers solder and a chalk line)
My first Jota had small web wheels, and the front needed a lot of weight to get it balanced, or it shook the bars at higher speeds; the second time I had the tyre off, I tried to balance it bare; it was well over 100g out!