Obviously an altcoin would have to be as much better than Bitcoin (in the ways people care about) as Bitcoin was better than the preceding stuff. A system that is decentralized and doesn't require mining could have this property.

How would coins become valued without mining? Isn't this the way that bitcoins actually become valued in terms of existing currency?

No, mining just prevents double-spending. The value comes from elsewhere.

People spend money on mining - power, equipment, time. This amounts to them buying bitcoins (from the set that haven't been mined).

This gives bitcoins a value in terms of existing currency (dollars etc.).

They might accrue value in other ways (how?), but does this process not bootstrap the bitcoins into having some initial value?

"does this process not bootstrap the bitcoins into having some initial value?"

No, because nowhere in that explanation is there any mention of demand for the mined bitcoins. If nobody were willing to accept a Bitcoin payment, the cost of Bitcoin mining would be irrelevant because the value of Bitcoin would be zero.

Ah, now I think I get it.

It is demand pull, not supply push - the miners are only willing to spend money on mining because they think they can get that money back by selling.

Buying mining hardware is speculating on the future price of bitcoin.

> What makes the current situation different?

Bitcoin.