It’d be the equivalent of a coal power plant halting using coal for a few weeks so they could shovel in trash from a nearby landfill until it was empty. Less overall power output for less profit.

not quite, since you have to reprocess the fuel, and the problem is that it's cheaper to just manufacture new fuel, so it doesn't make any financial sense. What's more likely is modern lead/salt cooled reactors using new fuel, and burning it past what we burn existing fuel. And potentially subsidizing waste reprocessing to burn it as well.

This is also ignoring the refueling operation being standard procedure. So it's more like a coal plant shipping in trash, which requires finding a source of trash, and one in a large enough quantity, and then burning it through the coal plant (without having to shut it down) and then having to find a source for coal, afterwards. It's just tedious.

It's also not "less overall power output" because again, the nuclear plants are simply designed with refueling in mind. So that's just an unfair comparison.

even if it was fair, nuclear plants have a capacity factor SIGNIFICANTLY higher than most fossil based production plants, and as a result, produce energy more efficiently and reliably over their lifetime.