There was/is some debate whether radial ply tyres are good for motorcycles at all.
When originally introduced, radials were very "squirmy". Radial ply construction enabled thinner sidewalls, which contorted, allowing tread to stay on the road surface, giving a higher threshold for breaking surface grip(the point at which the tyre breaks free of the road surface under lateral force). But, breaking free under greater force meant less predictable handling. Bias ply had firm, thicker sidewalls and a lower, but more predictable breaking point.
These factors were problematic for motorcycles.
First, on motorcycles, a flexible, distorting sidewall worked badly with lateral forces in cornering, and worked badly with thin bead spoked wheels, Cornering on bikes involves angling the tyre. This means creating an apposing force which moves the tread to the outside of the turn, and the bead to the inside of the turn. Moving the tyre surface outward has a negative effect on traction, and moving the bead inward has a negative effect on strength. Because radial tyres increase this distortion with their thin sidewalls, radial tyres were generally bad for motorcycles
Second, a sudden breaking point instead of a predictable one, meant it was difficult to tell when a tyre would start to slide around a corner. By the time the tyre broke, the bike was going too fast to correct. A rider had a better chance of catching a slide earlier and correcting, on bias ply tyres.
Finally, adding strength to the centre, was not easy on a rounded crest. Bias ply construction, meant rather even sidewall and tread area thickness - ideal for a rounded crest. Not so with radials. Tread plys in early radial tyres separated easily and could not hold a curved tread properly.
Radials for motorcycles were introduced successfully only very recently (Pirelli and Michelin, 1980's) and were still somewhat prone to these problems. To fix this, they were given thicker sidewalls and fewer tread strengthening plys. (One might say, "the worst of both worlds".)
Today, radials are made with stronger and thinner carbon fibre material, which enables the makers to add back non-separating tread plys, to thicken the tread area while still keeping it rounded, without detracting greatly from the sidewall performance. In other words, motorcycle radials are a crossbreed of bias ply and radial ply design. Unfortunately, they lost something with the compromise, and what makes radial ply construction good for cars, is exactly what makes it not so good for bikes.
