i had exactly the same problem with my 172 i had a fault powersteering
pump it was totally f@*ked!! at 64000miles it made a loud whining noise on full lock and cornering, roundabouts etc.
the answer to your question is yes it is expensive the pump alone is £240!!
i had it supplied and fitted for £488 there was i guy on this site selling one secondhand for a lot lot cheaper but the specialist garage i took it to would only fit parts that they supply.
i would recommend doing it asap as the bearing in my pump was F*&ked and could have gone any second! plus you dont know what other damage it could cause if it decides to cease and snap the auxbelt ie go into the cambelt!!!!!!!!!!!!!!
the engine on mind sounds better and quieter than when i brought it on 29000miles!! i had my cambelt and auxbelt full kit changed on mine at 47000miles and had no trouble with my powersteering pump until 64000 so i dont think this is a factor
hope this helps