Well I just checked satoshidice:
3613.54081797 BTC liquid cash = 1.3 MILLION $
They can run away with it any second now, yet they havent in the past 3 years (and back in 2013 that was worth much more).
So I think that is just paranoia, I think Satoshidice is very safe, and trustworthy.
Chances are will they? No they are running profitable... so they do not want to ruin that. It is a true money making venture.
I like a little more regulation then what gambling sites provide. But not everyone wants that so it all depends on your risk your willing to do on investments.
I dont think they can get away with stoling that much.
Your little regulation wont help at all in that case. Either they steal it and they get away with it (hard to believe) or they get caught.
Either way your regulation wont help at all, only the police after they get caught if they do it.
So your regulation has no benefits, but it can definitely scare away many gamblers as their privacy would be hurt.
No i dont think any regulation is needed here.