They aren't useless the secure the network.
If you decide to open a bank so you pay a contractor a lot of money to build a secure vault, and then you install lots of cameras, pay for an alarm system, and hire security guards .... and then the bank never gets robbed (maybe because the security is too tight) was it a waste of resources?
So are you saying that the process of mining is purely validating transactions? I apologise for my question if that is the case, I had the impression most mining calculations were akin to brute force calculations looking for special numbers that match the formula - similar to hunting for prime numbers. Have I got this all wrong then?