Actually it wouldn't trickle charge them, but it would start reverse charging them, once they run down to zero- That's not good for any battery type, and is generally what kills the rechargeables in a pack. (That's assuming the device uses the batteries in a series configuration; if they were connected in parallel, which is rare, it would tend to equalize the cells as you said.)
Just changing some of the cells can be done in an emergency; as long as you don't run them down to the point where the weak cells are discharged, it should be okay. The problem is that it may not be as apparent when that happens, because the newer cells may still continue delivering enough voltage to work the device.
By replacing all the cells at the same time, the point where they all poop out will be more obvious, since they'll tend to go about the same time.