Spinners, in of themselves, are quite destructive but there are two things which may help here:

1. In the UK Live Events scene, the maximum speed a spinner can get up to is 125mph in either the HW or MW categories since the only arena that can hold them (Extreme Robots) is considered a Class 2 arena. The arena you may have seen in the reboot of Robot Wars (series 8 - 10) was a Class 1.

That doesn't mean spinners can't cause damage of course, the speed limit is for safety reasons. A well thought out design and suitable armour material will help but damage, when facing any robot (not just a spinner) is largely inevitable.

2. As alluded to above, Extreme Robots is the only arena that can handle spinners in any weight category at all. Robots Live! is a Class 3 arena and thus, spinners aren't permitted so you won't necesserially see them at each event you go to.