> The only place I know of where °C or °F are used anywhere but temperature points and in deltas is in talking about specific heat capacity, which is usually written in J/(kg °C) even though that's the same as J kg⁻¹ K⁻¹. There may be some other weird units (like the aforementioned ns/√km or kWh/1000h), but nothing that would be as widespread.

I think you are very close to the same realization that I have.
Lets push this a little bit further.
Lets say you wanted to define an absolute quantity with units J/(kg °C) what does that even mean?
How do I convert a quantity_point in J/(kg °C) to a quantity_point J/(kg °K)? (which you can do with every other unit)
Do I
X J/(kg °C) = X J/(kg °K) + 273.15 J/(kg °K)?

The answer is... no one would ever do this!
Every single time that you see °C combined with any other unit (like in J/(kg °C)) it always means the same thing as Kelvin.

The only situation where you have °C and it is at an offset of 237.15 from absolute zero is when you are talking about an absolute temperature, a nowhere else EVER!

A temperature of 15°C does not mean the same amount of stuff as a difference in temperature of 15°C.
These 2 forms of °C are completely different units that apparently share the same name. It's a classification error! They are not the same thing!
Because the difference between two temperatures expressed in °C is not a temperature in °C, it's a temperature in Kelvin! It always has been!
But scientist are humans and also get confused!

Stop them from ever being able to represent °C anywhere other than an absolute temperature, and they will never be wrong!