Does anyone else run into the issue of players constantly wanting to level up?

Typically I do milestone leveling, but sometimes big events happen one session after another and I don’t feel like a level up is called for. I find that after 2 sessions my players are constantly begging for a level up. I even got this question earlier today: “Why are you so greedy about level ups?”

For story-oriented campaigns where fighting is common, what are your expectations both as a DM and a player for leveling up? I hear things like sessions equal to level then level up, things like privately keeping track of XP but not telling players, etc. No suggestion, however, aides in handling impatient players who just want to become powerful. Which is cool! Let them feel powerful! But already at level four I have issues balancing their battles - it is never a close call for them, but complete obliteration of my NPCs and creatures.

Do others have this issue as well? And what is your solution? Most of the time my players are excellent and they have even begun to roleplay more and more every session - but constantly have qualms about the lack of levels as if this is a video game and not a story-telling experience.