I don't think it's socially unacceptable to hire someone or purchase something for the benefit of a friend in general, especially if you are in a better position to do so than the friend (e.g. you run a service company in that field or are much wealthier than the friend).

However, in the particular case of moving, a friend might not want an untrusted stranger handling their belongings, so you would need their consent and they might not give it.