It's certainly more feasible to rent if you don't have the money to buy a house, which is why every single renter i know is doing do. I'm just not sure why this is necessary or a valuable economic innovation that justifies the rent paid.

Rentals are a useful innovation because the transaction is beneficial for both parties.

The leasor turns their large investment into a stream of payments, and the leasee turns their stream of payments into use of a large investment without having to make such an investment and without needing to have the capability to make that investment.

Avoiding making a large investment in property makes it easier for the leasee to move if needed, since there aren't significant costs to unwind a lease like there are to unwinding property ownership.

You're not sure why it's a valuable economic innovation that people who don't have the money to buy a house can rent one? What alternative are you suggesting, that they should get a house for free?

But the price of buying a home would be a lot lower if there was no rent (or other ways to own a home you don't live in). There are more homes than there are people.

Just about every 4-plex and apartment building in the world wouldn't exist if there was no rent to pay for their construction.

(On a much more minor note, there are not more housing units (about 140M) than people (about 335M) in the US and probably not in the world; though that's literally what you claimed, it's probably not what you really meant to claim. Taking the most charitable re-interpretation of your claim: there are slightly more housing units than households (about 140M vs about 130M) in the US. See above about the prediction that many of these housing units likely not existing [or continuing to be offered/maintained] if rent were outlawed.)