You're over-estimating the impact entirely, yes. The assumption that advancement in Monster of the Week is a matter of increasing power isn't correct. In the vast majority of Apocalypse World engine games, advancement isn't climbing, zero-to-hero Campbellian stuff. Monster of the Week is no exception.
Instead, advancement is largely outwards and only slightly upwards. The power level of the game is extremely flat. PCs gain new options, and their existing options get slightly more reliable, but they don't get significantly more powerful. Some advancements do nothing at all for power! Characters start out fairly capable, so though power does increase slightly, it's will never be more than a small relative increase against the baseline of a starting character.
That's why Apocalypse-based games put advancement completely outside of the Keeper's responsibility: it's neither your concern nor job to worry about balance or power level, because nothing you can throw at them can be accidentally out of their league or too easy, and they can never advance so far that the events of a session become inappropriately scaled.
So don't worry about it: the game has got this for you already. The advancement system ticks away and takes care of itself, giving the players new things to play with or new reliability for old toys, but never fundamentally altering the flat power curve of the game. Fresh-faced characters can play beside hoary veterans with dozens of advancements, and they will both have equal ability to contribute and grab spotlight — that's how not-a-problem the advancement rate is. In practice it will be somewhere between none (if they're avoiding opportunities to be awesome for fear of failing) to one or two advancements per PC per session, but it's highly variable due to the organic, improvised way sessions go in directions nobody (not even the Keeper) can predict or control — and, again, is really not the Keeper's concern.
In my experience, you don't ever have to even pay attention to advancement in a way that's typical for other games. The Keeper's job regarding advancement is only these two things:
- Help the players remember to mark XP when they trigger it.
- Keep yourself informed when they gain a new move, so that you can help the group notice when it triggers.
(Not so you can compensate or account for it preemptively — you don't ever need to do that! Remember your Agenda and Principles — they don't include “challenge the players”!)
Let the game work as designed, which is to exclusively let players worry about their PCs' advancement, and you'll see that it works just fine. Besides, you have way more important things to occupy your attention with during and between games, and it's a waste to fret about something that isn't even your job in a Powered by the Apocalypse–based game. Save your energy for the jobs the game does give you — you'll have your hands full!