My major concern with this is that vast majority of coins might reside in cold wallets and won't be able to participate in signing. So this technique encourages users to hold large amounts of coins online without password protection or otherwise prompt user to enter password while he/she might be asleep.
Also miners/pools might be hesitant to accept this change where they would share the profit with some random guy on the network.
Other than that I read the proposal and I find it interesting to at least keep brainstorming it.
One more concern about the whole idea - the "black hole" effect.
If one person or small group of wealthy persons gain control of both hash power and large amount of coins
(one usually leads to another) they eventually can overtake the network and take full control of it.
We might end up with Rothschilds of Bitcoin/Litecoin who will be able to build the best chain of any length almost for free.
With just mining to protect the network, wealthy people usually tend to get lazy and they would need to SPEND their precious coins on a new hardware only to gain ever decreasing amount of coins which might not be profitable in the end. While new generations of energetic people with little wealth will be eager to work on advanced mining equipment and BUILD the stuff themselves to get the remaining coins and thus maintain a healthy network.
Again considering that only a fraction of all coins will be in online wallets, all the attacker needs to do is to have enough coins for signatures to compete with the live wallets on the network, not the whole coinage in existence.