You can leave the fridge running if the ambient temp is 50C if you like. You might find that at these very high ambient temperatures most domestic fridges will struggle including the
S4 and will have close to 100% duty cycle. You might find that at this high ambient temp the temperature of the kegs will climb very slowly then overnight when the ambient temperature drops the fridge will catch up and then get back to temp. If you have the fridge full of kegs the fluctuations in temp might not even be noticeable.
It doesn't really harm the compressor that much. The thing that wears out the compressor more significantly is really the number of compressor starts. If you do connect an Inkbird controller to the compressor directly I would be very careful to make sure you have a compressor start delay of 2 minutes and also have at least 1C degree temp hysteresis and realistically 2C would be fine. I know a lot of home brewers like tighter temp control and you might feel tempted to make the hysteresis 0.1C or something but honestly your kegs don't need this level of accuracy and you will just burn out your compressor much faster as you will have a lot more compressor starts. Really the air temp inside the fridge might swing by 2C temp hysteresis but that doesn't mean the core keg temp is swinging by this amount.
So knowing that it's a compromise between overall compressor life and accuracy of temp control what do you guys feel would be an acceptable default temp hysteresis? Most domestic fridges and freezers have about 2C hysteresis.