And let's not forget that some NCR troops might kill legion soldiers and loot the money out of them. So accepting legion currency is also a good way for underpaid troops to still have some coin to spend on the Strip.
Legion currency is backed like NCR's (maybe even more as Legion coin is worth more than NCR bill). There's also a flow of their money from all those traders that trade in Legion territory.
I think that was a game design oversight.
Now that's a good question. I cannot remember if there's answer for this.How does The Courier go through Vault 22 without having any ill effects whatsoever?
The logs from Keely suggest that the spores from the lichen-covered scientists in the vault are not contagious to ghouls, but that's it.