Yes! I always thought it was ridiculous that the finder bracket could only be loaded from the bottom, and there is only a safety to stop it from falling upwards!
but not from falling out if it came loose.
But the thumb screw tightens up securely, so no issues have arisen.
If your thumb screw does not tighten up (hence your reported wobble) then maybe its not the correct size.
It should tighten firmly and still have more thread left over.
There has to be someone with similar setup living close to you, I suggest you try to compare their setup to determine what is causing your issues.
In the meanwhile, I agree some sort of fail-safe system would be good.