If they're internal doors then of course you do not have to finish them if you don't want to (why?). It's just wood.
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I have one in my house that I never got around to varnishing, it's looking a bit grubby around the handle now and I'm going to sand it and varnish. Would have been easier for me to do this when the door was new and I wish I had.
You don't have to do anything if you don't want to but my first thoughts were that eventually the oils from your skin would impregnate and start looking grubby and you say its already happened, sanding it may not even remove all if it either, better to seal and wipe clean I'd of thought