How's it work if you own the house (purchased by a transfer from ??? to your lawyer) and then sell it (funds sent to your lawyer and then to ???) ?
Probably couldn't get a US mortgage without that tax ID or bank account.
If you rent it out, I guess the contract should be with the LLC and then you run into the tax ID/LLC issues, but people will probably sign a lease with whomever and pay whomever they're told (whether it's the LLC or not).