Cryptocurrency is backed by the same thing as any other currency: popularity and consumer confidence. Whether such sentiments are "warranted" or "deserved" is a subjective matter, but that is irrelevant to determining its economic influence - enough people have invested in it for network effects to all but guarantee its continued relevance.
I'm on the pro-crypto side, but the US dollar has more than consumer confidence, it has the largest armed forces the world has ever seen. So a better comparison is something like gold, I think, that has value because we say it has value (it's shiny! and rare...)... which is fine, just different.
If I were a speculator, that instability would be attractive. But I'm not.