The question is, does it add a little more stability or not?
Whether it does or not, you have not come up with a way to incentivize it, and thus no one (rational) will do it.
I agree. The incentivizing aspects need to be discussed.
My first thought is that similar to what you suggest for distributing new coins to transactions and accounts, it can be modified to transactions and locked coins, maybe weighted by how long they keep it in freeze.