One reason I prefer to have the feed in the run (or with a larger coop and larger flock, in both places, is that the feeder and waterer take up valuable space in the coop -- at least 1 square foot for each, more if the feeder/waterer is larger. Space a chicken can't stand in doesn't count when you're figuring how many birds the coop holds appropriately.
I have not had a problem with vermin in the feed in the run -- possibly because I use electric poultry netting and have no active farms nearby.
You can try leaving it and see what happens. No one-size-fits-all solutions for chickens.