For some it is not a balance issue. We had a sixty page argument on whether an extra +1, 5% or less, was overpowered. Again, for some. Not everyone. For some.
I never said they can't climb down stairs. It is difficult for them. Maybe even it's not that difficult for centaur, that has a centaur brain. But what about the staircases Oofta pointed out? What about a shanty inn of poor construction? What if there is danger at the bottom of the stairs? What if someone is chasing the centaur? What if the stairs are in the dark? What if one of the stairs has has a bunch of children's toys sitting on it and the centaur needs to get down the stairs immediately? These are all scenarios. All of them the DM adjudicates whether the centaur rolls or not and how difficult it might be.
If the centaur walked down the stairs with no worries and was just going to his room in the inn that wouldn't be suited for him anyway (because a modified version where they deal with centaurs would have a ramp and a larger room they could rest in), I personally wouldn't even have them roll. But circumstances arise. In the example, I immediately thought of situations where they would roll. You obviously put it in a single context, the centaur during his leisure.
Ah, the dragon example. The stairs is a side note in the entire debate of centaurs. It started out as rope ladders and climbing cliff walls. Let's remember the posts about goats and RAW. Then, when it turns out the centaur restricted side said, "whatever works for your table is ok. But, as a DM I should be allowed to make the call that a centaur can't climb a rope ladder to the crow's nest." Then 20 pages later it is the pro centaur side saying, "So now they can't even walk up and down stairs." No mention of it being a table by table decision.
I would say this is endemic of this entire thread. Petty has a negative connotation. It implies the petty person is wrong if they make the centaur roll. Hence, any DM that chooses to run their table where the centaur is at a penalty (EDIT: By penalty, I mean having the centaur roll) while moving up and down stairs in an inn (which everyone pictures differently) is badwrongnofun.
One side says, whatever works for your table. The other side insists their way is correct, and if it isn't then the DM (or DM and players in this example) are petty.