You can get plastic solvents from serious shotgun suppliers. Keep them away from stocks or anything that's finished with something other than blue, parkerizing, or similar.
You don't need to clean your gun every 4 boxes. It can't hurt to boresnake the thing.
There's much to be said for a break-action shotgun. Easy to clean. There's even more to be said for fixed barrels. Choke tubes are an unmitigated pain in the ass when plastic-fouled.
Plastic buildup CAN impact accuracy, or really patterns. But not after a few boxes. After a few
cases, a wad-fouling cleaning is probably due.
But yes, you should pay attention to the insides of your shotgun barrels. If there are any moisture issues where you live (humidity, drizzle, snow, condensation) you should address that immediately.
Chamber condensation can be a real problem in some places, even desert places, where you might shoot the barrel hot, leave the gun in a rack and go inside for a snack while the outside temperature drops. I've found the insides of barrels coated with a layer of water! (For some reason, Brownings have a reputation for this, but it can happen to any gun. The wettest gun I've found was my Beretta. Maybe the rap Browning got was because they had plain steel bores instead fo chrome.)
I'm a lot more anal retentive about putting a coat of Rem Oil in the bore after shooting than I am about cleaning all the fouling out.
Rust is the enemy; plastic is just a small nuisance.