Forgive me if this idea has been suggested before, but I made this suggestion on reddit and I got some feedback recommending I also bring it to this list -- so here goes.
I wonder if there isn't perhaps a simpler way of dealing with UTXO growth. What if, rather than deal with the issue at the protocol level, we deal with it at the source of the problem -- the wallets. Right now, the typical wallet selects only the minimum number of unspent outputs when building a transaction. The goal is to keep the transaction size to a minimum so that the fee stays low. Consequently, lots of unspent outputs just don't get used, and are left lying around until some point in the future.
What if we started designing wallets to consolidate unspent outputs? When selecting unspent outputs for a transaction, rather than choosing just the minimum number from a particular address, why not select them ALL? Take all of the UTXOs from a particular address or wallet, send however much needs to be spent to the payee, and send the rest back to the same address or a change address as a single output? Through this method, we should wind up shrinking the UTXO database over time rather than growing it with each transaction. Obviously, as Bitcoin gains wider adoption, the UTXO database will grow, simply because there are 7 billion people in the world, and eventually a good percentage of them will have one or more wallets with spendable bitcoin. But this idea could limit the growth at least.
The vast majority of users are running one of a handful of different wallet apps: Core, Electrum; Armory; Mycelium; Breadwallet; Coinbase; Circle; Blockchain.info; and maybe a few others. The developers of all these wallets have a vested interest in the continued usefulness of Bitcoin, and so should not be opposed to changing their UTXO selection algorithms to one that reduces the UTXO database instead of growing it.
From the miners perspective, even though these types of transactions would be larger, the fee could stay low. Miners actually benefit from them in that it reduces the amount of storage they need to dedicate to holding the UTXO. So miners are incentivized to mine these types of transactions with a higher priority despite a low fee.
Relays could also get in on the action and enforce this type of behavior by refusing to relay or deprioritizing the relay of transactions that don't use all of the available UTXOs from the addresses used as inputs. Relays are not only the ones who benefit the most from a reduction of the UTXO database, they're also in the best position to promote good behavior.
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James G. Phillips IV 
"Don't bunt. Aim out of the ball park. Aim for the company of immortals." -- David Ogilvy
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