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No, even if you only had one unit for a physical quantity, you would still need to specify that unit to know which physical quantity you are describing. E.g. “That object over there is 15” vs “That object over there is 15 kg”.
The symbol for temperature, measured in Celsius, is “°C”. It’s atomic and can’t be separated, since that would result in °, which represents the angle of something, not the temperature, and C, which is the symbol for Coulomb, which measures electric charge.
I disagree, and would argue that both are about equally frequent. For example, my phone shows °C in the weather widget, while the weather app only uses °. That does not change the fact that the actual unit is °C, and that would not change even if the whole world switched away from °F, and your original comment about the display having °C implying that °F still exists is therefore incorrect.