Grace isn't kidding when she says it's part of her cool robot therapy. The in-game explanation for leveling up is that the main character, Adam Jensen, already has everything you could get by leveling up built into him. He can't access it all right away, however, because his system wouldn't be able to handle it. Experience Points essentially represent Jensen's system becoming better able to handle using more of what's already built into him.
End result? Doing stuff like breaking into the employee offices of the company you're the chief of security of literally functions as physical therapy for Jensen.
As for stealthy missions, you get a bonus for not being seen that is equal to knocking out ten enemies. You can still knock out enemies and get that bonus, however, so you're incentivized to sneak through unseen while knocking out everyone you can anyway. You're also incentivized to crawl through every air duct, for they may count as exploring, which is even more XP. The player is heavily rewarded for behavior that makes no sense given their objective.
I mean, sure, it's more fun that way, but that's not going to stop me from pointing out how ridiculous it is.