Once quantum computers are possible, is there actually anything else, any other real world applications, besides breaking crypto and number theory problems that they can do, and do much better than regular computers?

Yes, in fact they might be useful for chemistry simulation long before they are useful for cryptography. Simulations of quantum systems inherently scale better on quantum hardware.

https://en.wikipedia.org/wiki/Quantum_computational_chemistr...

One theoretical use case is “Harvest Now, Decrypt Later” (HNDL) attacks, or “Store Now, Decrypt Later” (SNDL). If an oppressive regime saves encrypted messages now, they can decrypt later when QCs can break RSA and ECC.

It's a good reason to implement post-quantum cryptography.

Wasn't sure if you meant crypto (btc) or cryptography :)

From TFA: ‘One more time for those in the back: the main known applications of quantum computers remain (1) the simulation of quantum physics and chemistry themselves, (2) breaking a lot of currently deployed cryptography, and (3) eventually, achieving some modest benefits for optimization, machine learning, and other areas (but it will probably be a while before those modest benefits win out in practice). To be sure, the detailed list of quantum speedups expands over time (as new quantum algorithms get discovered) and also contracts over time (as some of the quantum algorithms get dequantized). But the list of known applications “from 30,000 feet” remains fairly close to what it was a quarter century ago, after you hack away the dense thickets of obfuscation and hype.’