I assume that common warning about doing the final rinse/stabilizing is rather caused by the idea that after hanging films for drying one could forget to rinse the reels at all, than by any fact of hard to get-off residues of the last bath.
But even then any residues should be rather harmless. Formaldehyde (if used at all) will have evaporated and wetting agent and biocide should be low in concentration or harmless as such. Though one can argue about that.

So yes, if you are afraid to scratch wet film whilst unloading, keep them in the reel for the last bath.