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.
I can tell you as a real estate agent I almost always recommend to my clients that they leave the appliances... appliances are a pain to move! No guarantee that your old appliances will fit in the respective places in the house you are buying, likelihood of beating up the walls and floors as you move them in and out of houses, and often it will cost you as much to move it as it would to just buy a new one. Further - the buyer of your home generally doesn't want to have to go spend thousands on new appliances right after they dropped a big chunk of coin buying your house. It definitely makes an impression on buyers, especially how petty it looks if you are marketing a luxury home where the sellers have stripped all the appliances - does not give the impression of luxury to a prospective buyer.
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.
Why would they be paying to move it at all though when the house they are buying already has perfectly good, and often better, appliances than they would be moving anyway.
Dude - consider mainstream buying options like say, Costco, Home Depot, Lowes, etc. There are apartment sized refrigerators going for nearly $1000. Can you find a super low end model for under $1K? Sure - but that's not what the majority of people are putting into their homes for a family unit of 2+ people. Can I throw a washer and dryer into the back of my truck? Sure - but that's not what people are going to do if they are moving outside their immediate vicinity. At minimum they are backing up the U-Haul, at the high end they are bringing in movers.
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.