No Harold, the problem is that you don't really understand property law. Ownership carries with it a whole bundle of rights. If you don't have that bundle of rights you don't own it or effectively own it. Among the most important property rights are the rights to sell or lease the property, the right to destroy the property and, for personal goods, the right to take possession of it and move it around. The mailbox on my house is not owned by the USPS, nor does it effectively own it. Why? Because it lacks those important rights in the mailbox. The USPS cannot sell my mailbox. The USPS cannot lease my mailbox to someone else. The USPS cannot come to the house and remove the mailbox, destroy it, or move it someplace else. Because it lacks some very significant rights that an owner would have it clearly is not effectively the owner of it.
What can the USPS do? It can tell me that if I want to get mail my mailbox must meet the requirements specified in the postal regulations. That does not make the USPS the owner of mailbox any more than the city telling me my home must meet certain building code requirements would make the city the effective owner of my home. The USPS can also refer to the DOJ cases for prosecution if someone were to grab the mail out of my box and destroy my mail or were to open my mail without authorization. But that also does not make the USPS an effective owner of the mailbox any more than the city would be an effective owner for prosecuting someone for vandalizing my mailbox.
If you want your mail, you need to make your mailbox meet USPS standards. If you don't want to get convicted of a crime, don't take someone else's mail. But while federal law covers those sorts of things, they don't provide the USPS with anything close to the bundle of rights in the mailbox that an owner would have.
You can say you're not having it all you want. But that doesn't change the fact that you clearly overstated matters when you said that all mailboxes are owned by the USPS. And even coming back to amend your answer to the USPS being the "effective owner" fails for the reasons I just described.
Just because the USPS doesn't own my mailbox and isn't the effective owner of it doesn't mean that it doesn't have rules that impact my mailbox. Clearly it does. Had you just limited yourself to saying that federal law does prevent the homeowner in this case from stealing or destroying the OP's mail I would not have had a problem with that. However, that's not what the homeowner is doing. The homeowner is taking the mail from the box and distributing it to residents himself rather than letting them access the mailbox to get their mail. Whether the homeowner is within his rights to do that depends on the answers to the questions I asked earlier.
I'm not going to address who owns your mailbox because it is a matter of semantics. Once a mailbox is installed on a dwelling or the side of the road, it's use is controlled by the USPS. They can make you replace it if it comes into disrepair (they can refuse to deliver mail to it). They can say it is too small for the amount of mail being delivered and needs to be replaced. So what does it matter who actually owns the mailbox? If it gets destroyed you need to replace it if you want mail delivery. You want mail delivery you comply with USPS regulations.
No one can put mail (or anything else) into a mailbox except a USPS postal worker. And no one can take mail out of a mailbox except the addressee. Addressee is defined as a person or business at that address. The postal regulations require a separate mailbox for every addressee. In an apartment complex, every apartment has its own mailbox. The same is true for condominiums. A landlord renting out rooms or apartments is also required to provide a separate mailbox for each tenant.
So to answer OP's question, if the landlord does not provide separate mailboxes for each tenant they are in violation of the law.
We have no reason to think this isn't a home that has some number of individual rooms in it rented out. The OP's language would point to that as the situation. Such a residence does NOT have to provide individual mailboxes any more than you or I have to provide individual mail boxes for every family member in the house.
If I were to live in such a place I would have purchased a PO box long ago.
I will simply disagree with you. A family is not the same situation as someone who rents out rooms to persons that are not related to each other. You can read the USPS regs that I posted a link to if you so choose.
A lot depends on the size of the city/town. If we're talking NYC, Los Angeles or Chicago yes, it's probably address only that control what goes in a PO box. A small suburban or rural town, not so much.