Cost. ~$5,0000.00 of cost for changing any of those brands you mentioned from counter depth to built in.

A built-in will be flush with your cabinets, will be very expensive, will require the proper cabinetry and special installation and may well lock you into that brand for replacement unless you're willing to redo the cabinetry. A CD will protrude from the surrounding cabinets at least by the width of the door, will be a lot less expensive, and can be readily swapped out for a different fridge.

My wife wanted a full depth ("standard") refrigerator, so we got 30.5" deep counters on that wall. Now, I can get a reasonably priced "counter depth" refrigerator, and have a great counter depth -- can have toasters, etc. pushed back, and still plenty of prep/working area. And 27" deep drawers instead of 21".

I was having trouble fitting a big sink on the other side of the "L", so I made that counter 1.5" deeper than standard. Standard depth cabinets, shimmed out from the wall.

Most built-ins are standard size and can be swapped out in the future for a differnt brand. 48" wide x 84" high or 42" wide x 84" high. A few are rather unique like Liebherr which is 80" high. I built a 4" wood grill over my Liebherr. In the future I can simply cut it out and get a standard size American built-in.

There are counter-depth fridges that have the option of custom panels.

Boxing in a standard refrigerator that is not meant to be built-in will not have proper ventilation.It will work harder,be noisier,use more electricity than stated on energy guide label,and fail prematurly. Having said that you can get several average price standard fridges for the price of an average built-in.CD fridges usually require a bit less clearance from cabinets/walls but look at the install requirements before purchase.

ADVICE: I would look at what most homes in your neighborhood have. If most have built-ins and you have counter-depth then that will be a significant negative for resale.If you get built-in and most have free standing you will not get any of your money back when it comes time to sell. Then again if this is your forever home who cares about resale; go with what your gut tells you.

After getting over the price shock, the panelled Gaggenau fridge is the nicest appliance in the kitchen. (it is the sister fridge to the integrated Bosch/Thermador fridges but has a nicer interior).
It is subtle as it looks like the rest of the cabinet panelling. It is quiet (silent) and keeps food amazingly well (far better than we expected) It is huge on the interior yet everything is accessible. The Gag come with a standard 5 year warranty and the insides are all stainless and aluminum. From every angle, it was worth the money!
If the budget can run to it, I would seriously consider it.
caspian