Yea, your first instinct is correct. So, depending on what you’ve done before leveling up you’d have different choices based on what you’ve checked. Then you erase everything and start over with making check marks. Of course as DM you could rule that players could level up a couple (or more) things at once if it made sense. You could also rule that players don’t need to erase check marks after leveling.
And yes, you’re right that there’s no value in splitting check marks. However, I found that players in many instances would have a lot of checks to choose from so it wasn’t ever an issue that they’d checked 3 things only two times for example.
Also, keep in mind that if you make some checks next to something weird on your sheet , the DM has to think of a way to level it. So I had one player make checks on a map or a note or something that they had in their inventory. So I gave them a more detailed map of the area and ruled that they then were more skilled at tracking and wilderness related things and could roll with advantage on those types of actions. I’d probably change that to an x-in-6 in the future but it worked out in the game.