I don't see the need for a thumb break on a CC holster, other than if you are going to be running, or jumping a lot. A well made belt slide will retain your side arm when bending over, etc, but a thumb break is always a bit more positive in the falling out category in rough situations.
That said, I have carried for many years with a belt slide open top, without a strap, and prefer it, not for speed(although that is a plus), but I have seen straps bind behind the hammers of others weapons, and don't like that idea.
Also, if it's for concealed, how would someone grab it from you?