Being rare and useful gives something value.
That's a given, though how much? And how much of that value is convention & faith?
That depends on the usefulness and the rarity.
That is however not the question here. The above clearly shows 'backing' is unnecessary. Bitcoin backs itself.
Are you saying Bitcoin's value is due to its rarity & usefulness? In that case, i'll release Bitcoin V2.0 -- identical to Bitcoin in every respect, but with just half the coins.
Backed by funds invested in mining rig and payment for the electric. As ASIC mining rigs are only build for BTC mining, those devices have not residual value, so I assume here that people pay cash for those devices are equal to cash flow into BTC world, look today more and more people joint to mining business, because the attraction of profitability. Therefore more and more cash are indirectly investing into BTC...if we assume that miner are rational they will only sells their BTC for profit...then ,the value of BTC will be secure by their rationality.