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.)
(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.)