When you book a move, you are dealing with one of two very different businesses. A carrier owns trucks and employs crews: they pick up your furniture and deliver it. A broker owns nothing but a phone line: they take your deposit, then sell your move to whichever carrier accepts it.
Brokering is legal, and some brokers are honest. The problem is that many advertise like movers, quote like movers, and never mention that a company you have never heard of will show up on moving day. If that carrier is overbooked or underpriced, your move gets delayed, renegotiated on the sidewalk, or worse.
Brokers earn the gap between what you pay and what the carrier accepts. A lowball quote feels great until the carrier, who is being paid less than the job costs, makes up the difference with extra fees at pickup. Most "the price doubled on moving day" stories start with a broker quote.
Check who you are really hiring before you pay a deposit. It takes one search.