I just looked back at an appraisal I did of a fee simple restaurant with an almost identical cooler and I did not include it. I came out a bit over $200/SF on a 2,000 SF franchise restaurant. The cooler measured 8'x14' and I considered it personal property. I just Googled it and found a similar cooler for sale delivered for about $10,000. Had I applied the same price per square foot as the improvements I would have come out at around $25,000. These things can be disassembled and moved so I would consider it a fixture/personal property and not include it in the building area when calculating lease rates or sale price per square foot. I would also check to see who owns it. Oftentimes I'll see restaurant leases where the tenant is charged extra because the landlord is providing some or all of the FF&E. That can range from completely turnkey to include all kitchen equipment, dishes, silverware, etc. to a hood, sink, and maybe a walk-in cooler/freezer. The latter may result in a lease rate that's $1-2/SF higher than a regular retail space while the former can command an extra $5-10/SF depending on the quality of the FF&E, size of the restaurant. etc.
You make valid points and I've gone the same route in the past. But, since I always accept the appraisal profession's consensus lying down, I'll mention why I think it could potentially be considered otherwise. First, you mentioned a difference in value of about $25,000, although obviously considering WICs on both the subject and the sales/ rentals would suggest a lower unit value. For example, if you appraised the property for $200/ SF without the cooler, it would be $189/ SF with, which would imply a proportional value of about $21,000. This includes land however, which may or may not be a significant portion of the whole. It also the cost to install, which can be a significant expense, and presumably not included in that Google estimate. Also, $189/ SF is effectively the average, so for example, if I appraise an office/ WH for $40 per square foot where the office portion is more valuable than the warehouse portion, the $40/ SF would be the ceiling, rather than the floor, for the contributory value of each incremental warehouse square foot. Third, if I appraise a hotel, looking at the salvage value of used FFE could potentially understate the contributory value of that component, as it is considered based on part of the whole and the market's reaction to 5-year-old FFE as part of the whole could be different than 5-year-old FFE being sold separately.
Another issue is what is there, assuming the cooler is removed: you have a big hole in the wall. In the appraisal that I'm working on, the implied contributory value of the cooler has a ceiling of $15,000 or so, based on its value as part of the whole using the premise discussed above. You have costs to uninstall it and add an exterior wall. Construction costs are often prohibitively high around here and though I don't know exactly how much it would be to build a wall, it would most likely be a good fraction of that $15,000. I've seen c-stores sell with their pumps/ USTs removed, as well as car washes sell without their equipment, but I don't recall seeing a restaurant sell with the cooler removed (I'm sure it's happened though).
A bit of a rambling post, but just sharing my thought process in attempt to reconcile views.