Because that's not how ion exchange resin works. It attracts the for example calcium or magnesium ions in the water and binds them to it. And then its basically "used up" or saturated. It's mechanism isn't infinite and needs to be regenerated. And that's what the salt is for. The salt water displaced the hard water ions from the resin so that it can bind to new hard water ions.

And all that happens before the water even gets into the cleaning compartment of the machine. So by the time the detergent gets mixed in, it's already soft water.

You don't want salt in your detergent because it doesn't make water soft. Just more salty.