I think long-term the chain will not be secured purely by proof-of-work. I think when the Bitcoin network was tiny running solely on people's home computers proof-of-work was the right way to secure the chain, and the only fair way to both secure the chain and distribute the coins.
See https://gist.github.com/gavinandresen/630d4a6c24ac6144482a for some half-baked thoughts along those lines. I don't think proof-of-work is the last word in distributed consensus (I also don't think any alternatives are anywhere near ready to deploy, but they might be in ten years).
I also think it is premature to worry about what will happen in twenty or thirty years when the block subsidy is insignificant. A lot will happen in the next twenty years. I could spin a vision of what will secure the chain in twenty years, but I'd put a low probability on that vision actually turning out to be correct.
That is why I keep saying Bitcoin is an experiment. But I also believe that the incentives are correct, and there are a lot of very motivated, smart, hard-working people who will make it work. When you're talking about trying to predict what will happen decades from now, I think that is the best you can (honestly) do.