Do subsequent playthroughs of Undertale get easier?

Solution 1:

How you play definitely has an effect on the difficulty/gameplay, but new runs don't have any in-game mechanism for making subsequent playthroughs noticeably easier or quicker that I'm aware of.

One of the main differences between different runs is your goal during each fight. This can change the encounters quite a bit. Trying to have a conversation with a monster without dying is obviously going to be different than trying to kill it without dying. So difficulty may change with how you choose to run the game, but not due to the fact that you have already beat it.

There is at least one small exception to this, where if you do the same type of run multiple times, you may not have to fight the last boss again; but I doubt that is your main concern.

So no, the mechanics don't get quicker in any noticeable way, or the fights any easier, due to subsequent playthroughs. The nature of encounters, and even the encounters you run across, can change quite significantly based on how you choose to do your run, though.