In summary, I have concluded that this idea is pretty much equivalent to having a POW bitshares.
Whether or not a POW bitshares would have any better price stability is another question... If all coins had to be POW burned into existance, supply would have started low (compared to 2B DPOS coins) and given a like for like demand that DPOS bitshares had at its inception I suggest that the price per coin would have been much higher at the time... Whether it would have held value is yet another question, though.
The key problem (for use as collateral) is redeemability in both cases; DPOS tokens and POW tokens cannot be redeemed for the things that created them. Now, if you could redeem DPOS tokens for BTC directly on chain, that might be a different matter, but sadly this is impossible.