You ask why it doesn't work. To make things simpler, we move Pd3 to e3 such that all tactics in the e-file become a nonissue. When does Bxh2+ work anyway? The standard conditions (obviously there may be myriads of concrete alterations when it works a different way than standard) requires:
A: You get your knight to g4.
B: You get your queen to h4 (or maybe ...
As you've shown in your analysis, the line after ...Bxh2 does indeed give Black a decisive advantage. However, Black also has a completely winning position without going for ...Bxh2, so why bother calculating the complications when there's an easy way to have a good advantage?
What's the point of the Greek Gift? Do you gain anything by decoying the White king to h2? If not (and I don't see any gain; in fact you lose a little since the final ...Rxe1 does not come with check), there's no need to give up the bishop; you might as well play 21...Rxa1.