I don't think we should set ourselves up for "a double spend is the end of the world". Payment reversals are so common in every other form of payment that "no reversals ever" is a standard far higher than it really needs to be. Miners are a way of managing risk. For instance, I think it'll be common in future for people to pass around free transactions without broadcasting them, until somebody in the chain of payments decides they can't totally trust the sender and broadcasts the entire chain, using the miners to lock it down.
Any given assurance contract is relatively small (for just one block). If the contract fails because nobody cares about that level of security, speeds will fall a bit until enough people care. It's self adjusting in that sense.
A double spend is the end of the world for Bitcoin in my book. One of the key features of Bitcoin is that it can't be messed with or manipulated. As soon as a double spend happens, then anyone who thinks about submitting a large transaction has to worry about it being reversed, either maliciously by the other party, or as a side effect of someone else doing a double-spend elsewhere. You (and any companies that deal with Bitcoin) would have to start tracking all spends and receipts to make sure none of it gets reversed. And with a blockchain that is lightly and very variably defended, as it would be in the case of assurance contracts, it'll be all the more easy for someone with malicious intentions to overtake it. If you only get 1 BTC per block in donations for your contract, then we suddenly only have 200GH/s protecting the network, which is a heck of a lot easier to attack and double-spend against than 8 TH/s.
I really don't think you'd find enough people volunteering to give up their Bitcoins to secure the blockchain. That's like allowing people to send in whatever they feel like contributing to the government come April 15th. There's a reason why taxes are forced, not voluntary. We all benefit from the uses of tax money, but we're not all willing to contribute towards those benefits voluntarily. Too many people just like to freeload on whatever is given to them.
Anyway, I'm still of the opinion that transaction fees will be the only way to support miners in the future. Hopefully, the number of transactions per block will have increased greatly by then, and the fee per transaction won't have to increase by much.
On that note, I wonder what would happen if someone released a modified Bitcoin client that doesn't drop the block reward, ever? Would more than 50% of people gravitate towards it and use it? I doubt it, but it's possible... IMO, that would be the best route to go, but it would surely be a disappointment to everyone who was looking forward to Bitcoin being limited to 21M coins.