About 22 years ago, I took the DIY approach on my workshop floor. It was previously painted gray and had areas of missing paint very similar to what is in your picture. It's now two decades later and there is one small area, about 6" inches square where one large chip has developed. It is in a high traffic area and it is all the way down to the concrete surface. I'm assuming it was one of th e areas that was covered with paint and the paint finally lost adhesion to the concrete and the epoxy strength finally gave out so a blister formed and the chip finally came off. Other than that, it has remained rock solid. Overall I have been very happy with how it has performed. Of course, there are lots of variables that can affect the long term performance - who knows, maybe I was just lucky.
I started out by scraping the edges where the old paint had chipped, then I mopped and rinsed the floor thoroughly a couple of times. I followed that with a product like Rust-Oleum's Concrete & Garage Recoat Primer which is made to seal and prime previously coated concrete. Then I used the Rust-Oleum Epoxy Shield Garage Floor Coating Kit which included the base coat (gray), paint chips (white, black, blue) which not only provide aesthetics, but also provide better traction, and a clear topcoat. There was also an etchant in the kit, but I didn't use it since I used the Recoat Primer instead.
I don't know what professionals would have charged, but for my shop it cost me something like $60 for the primer and about $180 for two Epoxy Shield kits (I needed two for the area and because I only did one half at a time by moving equipment first to one side and then to the other). Along with disposable brushes, rollers, roller pans, and other miscellaneous stuff, I probably spent about $280 - $300 for the whole project.
I only wish they sold a smaller kit so I could patch the one bad spot that has developed. I have been hesitant to spend a hundred dollars just to patch a small 6" inch area. If we ever decide to move and put the house up for sale I will break down and get one so I can fix that one small spot up.
I don't know about the refrigerator, but I do know that Rust-Oleum makes an Appliance Epoxy paint that is formulated to refinish appliances. It sounds like a lot of work with all of the prep that would be needed, but think the paint is only about $30 for a quart.
Regards,
Dave