Don't people bring their appliances with them when moving?
When you make an offer to buy a home, there will be a section that lists the furnishings/appliances/things-not-nailed-down that are included in your offer. Your real estate agent is going to check the boxes for appliances without even asking you. You could tell the agent not to do that, and the seller could say no. But that would be unusual.
A new refrigerator is roughly $1k for a cheap one, don't tell me someone is going to charge more than that to move a single item. Hell, I've paid for an entire move for less than that.
I live in the US and I don't know of anyone who chose not to bring their appliances with them.