Yes, this is a thing. As you can see here, there’s a lot off folks who do this and it works out.
Just something to keep in mind—you have to realize that running your startup and being a landlord will be separate situations. You just have to be as transparent as possible so there’s not even the appearance of impropriety. Just keep it all kosher and there shouldn’t be any issue. Like you mention, you don’t want to be accused of using your power as a landlord to take advantage of your startup. It kind of shoots yourself in the foot, plus it won’t bode well with any other business that rents from you. And yes, you’ll want to make sure the board approves this decision, but that’s pretty much a given in a C-corp.
If you are interested in other legalities surrounding startups, check out my eBook. It’s a free resource for folks in the startup industry who may be looking for some answers to common legal issues. Hope it helps!