I can see where people are coming from with regard to adding thermal mass for the purposes of stopping the compressor kicking in everytime you open the door when you are retrieving a beer from an upright fridge, that makes sense. With a chesty being operated as a keezer I dont have this issue because:
a) you dont open it often, and
b) even when you do, the cold air doesnt pour out like it does with an upright.
However do regular fridges and freezers have their regular thermostats sitting in some sort of thermal mass? I would think they would work on the same principles as the STC with the built in min and max settings and compressor time lag safety setting? Wouldn't you expect the compressor to kick in after you retrieve a beer and all the cold air escapes, just like you hear the compressor on your regular fridge kick in when you leave the door open for a few seconds?
However, this to me is just plain wrong. I can understand that you want the liquid a certain temperature, and the ambient temperature is not your predominant concern, yep, makes perfect sense. However the best way to control your liquid temperature is to keep the ambient temperature at the temperature that you want your liquid to be. In a keg freezer this is simple, just leave your temp probe in the open air within the keezer and set your min and max temps to a few degrees apart (one or two either side of your desired liquid temps) and the liquid will end up being correct. I can peoples point regarding your glass of water, but all you are introducing an external min and max to your controller by putting your probe in a thermal mass of limited size, accounting for any minor variations in the temperature between the top and bottom of your freezer by allowing the glass of water to keep a temperature relative to the air moving around it, ie the air may be 3 degrees warmer at the top, and 3 degrees colder at the bottom at any given point in time, however as long as you keep the air blowing around, and have a little thermal mass around your probe, this wont matter. I would argue that if there is a 3 degree variation between the bottom and top of your freezer, and you are circulating the air, then you could just widen the kick-in and kick-out temperatures on your temp control and it would do exactly the same thing, but horses for courses, both will achieve the same result.
Where you lose me entirely though is when you suggest that the air temp is unimportant and the liquid temp is what matters. It sounds to me like you would happily install your probe in a thermowell within your fermenter in your fermenting fridge (or inside your keg in your freezer if possible), and use this to run your temp control, because you are interested in the temperature in the liquid, not the ambient temp. This is just wrong. Yes, you are more interested in the temperature of the liquid, but no this does not mean that you want to have your probe inside your fermenter, or even emulate this by having it in water. The reason for this is that by the time your liquid reaches the desired temperature the ambient temperature will be well and truly beyond the desired temperature (ie the fridge will be at 2 degrees by the time the liquid gets to 20), then the fridge will kick out but the temperature in the fermenter will continue to go down to say 18 degrees because it will take forever for the fridge to get back up to warmer temps. If you have a heating element involved, that will then kick in, and bring the temperature in the fridge up to 40 degrees while it struggles to get the beer back up to 20, the heating will then kick out, but the temperature in the fermenter will continue to rise while the fridge tries to get back down again, and so on. So what you would have is fridge temps swinging from 2 to 40, and fermenter temps swinging from 18 to 23, this is hysteresis at work. Control the ambient temp within 3 degrees and the fermenter temp will scarcely vary at all. So even though you are more interested in controlling the liquid temperature, the best way to do this is by getting the ambient temperature as close to correct as possible. Obviously with a fermenter you might need to keep the ambient temps a bit lower than what you want your liquid to be due to heat from fermentation, but putting your probe IN your beer just doesn't make sense.