Housing shouldn’t be gatekept. Rent as we know it is broken. Someone owns a property, while you pay the mortgage. But you’re not paying down to own, you’re paying it down for someone else to own. Sure, renting is fine for people who move a lot, but that money shouldn’t be flushed down the drain every month—from the position of the renter. Rental credits, to where that money you’re putting down acts as a credit toward getting the opportunity to own. This would take a massive restructuring of the way we behave as a society, but it’s desperately needed.

making it illegal for corporations to buy residential property

It's not quite that simple though. What do you mean by "residential property"? Single-family homes? A duplex? Okay, that sounds fine, but what about an apartment high rise? That's a residential property, and there's not a great way to have it all be rental property without being owned by a corporation of some kind. Even when you talk about renting far few units--such as an owner-occupied apartment building with 4 units in total (these are fairly common in Chicago, which is the rental market I'm most familiar with)--a "corporation" may be something like an LLC in order to shield the owner from personal financial liability in case of catastrophic loss. (And yes, I'm aware that incorporating as a small business can and does get abused. In theory there are checks against that, in practice they don't help in many cases since there's too much going on for any municipality to go after every single case of business fraud.)

Of course, you don't want individuals owning vast tracts of residential properties either; that takes all the problems of corporations owning property, and concentrates them into the hands of one person.

I think that there might be a way to regulate and incentivize behaviour through tax policy, but I'm not sure what it would be. Perhaps a system that put a hard cap on profits, and required certain percentages of rent to always go into maintenance and improvements? You'd probably also want to exempt corporations that owned or had control over 6 or fewer units.

This would be a fun (read: complex and challenging) area of public policy to get involved in, because you want to make housing affordable, but you also don't want to disincentivize development.

Ninja edit: I'm saying all of this not because I'm pro-corp, or pro-gov't, but because any time you try and fix a problem, you're going to have bad actors that are going to try and break your system in order to get as much personal profit out of it as they can. Trying to find the weak points and then reinforcing them makes it harder for good ideas to be abused to a negative end.