To say someone is homeless is not assigning an identity, it's just describing the state they're in.
I'm overweight. To describe me as overweight is accurate, and I wouldn't think you were saying that it's my identity. To describe me as "experiencing obesity" just sounds silly and changes absolutely nothing.
The English copula is frankly a mess that does among other things, assign identity and class membership. It's completely ok to use a verb which specifically indicates class membership in an unambiguous way.
