3000 rounds? that doesn't seem like a lot to me. My O/U had fired over 30,000 rounds before I had it serviced. Everything worked fine, never had a problem.
A pump gun should give many years of use before something breaks. It would be pretty hard to wear out an 870, you might need to replace some minor parts but the gun should last longer than it's owner. I have heard of Gas operated semi autos wearing out to the point that the receiver cracked, but these guns were used by skeet shooters who put many tens of thousands of rounds through the guns for many years. Big thing with gas guns is to replace the recoil spring at regular intervals. The "Technoid" at
www.shotgunreport.com has discussed this many times.
If you replace certain parts on a routine basis the gun should last a lifetime.
Geoff Ross