Side question, In the introduction the author mentions that if you don't care about privacy, you can solve the x ∈ S problem easily by sending the whole bloom

Side question, In the introduction the author mentions that if you don't care about privacy, you can solve the x ∈ S problem easily by sending the whole bloom filter to the client. Wouldn't it be simpler for the client to send x to the server instead, and then let the server send the answer back to the client? As I understood bloom filters can get quite large...