Higher levels unlock more skills, which are usually dependent on factors such as number of enemies on screen and time left on stage.
As for the level scaling, I don't get it either. For some reason, the zombies I've been encountering on exploration, especially in the first couple stages, have so much more health and have huge resistance against headshot damage. It's messed up, especially when compared to the zombies I encounter on higher stages in annihilation mode, who are easily killed with one headshot. I think the annihilation mode zombies are scaled appropriately, but exploration seems to get ramped up hard.
But then again, it is a microtransaction heavy game that also heavily rewards viewing ads--there's an achievement for ads viewed. So maybe the difficulty scaling is appropriate for making you empty your wallet
Edit:
I just noticed that you already know about the stat bonuses. This leads me to believe even more that the leveling is pretty much arbitrary and the difficulty scaling serves to get players to spend more or watch more ads