I've sold, installed and serviced thousands of water softeners and can tell you a prefilter on most of them will eventually reduce pressure and gpm, which causes failure of the resin. Unless your water is visibly dirty, you don't need and shouldn't want a prefilter on the vast majority of water softeners.
The choice is yours as to what you want to protect, and I'd have to ask what that is because you aren't protecting the softener from invisible dirt. The resin filters that out and with proper water pressure and gpm flow, backwashes it out of the resin every regeneration.
ALL waters have invisible dirt. So what? The current cultural thinking that we would do well in a pristine environment, meaning our houses, water, hands and clothes so clean you can have no "germs" and could eat off the floor, seems IMO to be a leading cause of lots of kids and adults having allergies and other immune problems because of over protecting kids and ourselves from any and all 'dirt', preventing the body to build immunity.
If you are really into that ultra clean thinking, I suggest filtering the dust laden air you breath. Twenty five years ago who would have thought that people were so prone to paranoia that they'd pay like ten times more for a bottle of drinking water (per gallon) than a gallon of gas? Maybe the next big money maker thing is the face air filter... And trust me, many women and feminized men today would have their kids wearing one!
You look at the cartridge and see it getting discolored and think it is removing dirt, more likely is the trapped air in the filter cartridge oxidizing ferrous iron in the water which converts the iron to ferric iron/rust in the cartridge. Or a 3 month build up of invisible dirt found in all waters that you drank for how many years without problems? BTW, resin is a very good dirt filter, although you don't want to use it as such.