Shouldn't hurt anything, the length of time the compressor runs to keep the compartment at say 60 degrees in a well insulated freezer is a lot less than keeping it at zero, so the energy required is minimal. More likely, the freezer will suffer a mishap from poor handling, or a refrigerant line corrodes with age and starts to leak. Based on my own limited experience old freezers or refrigerators will often run for decades, then fail when they are moved or sit idle for a long time or a component like a thermostat fails, and the part is NLA or it is cheaper to just replace rather than spending a lot of money to try and repair an ancient appliance.
That being said, I am looking for a replacement of my grandmothers 30+ year old GE 10 cubic foot chest freezer I recently converted with an external thermostat. It gradually lost its fizz this fall, but hung in there long enough to cold ferment my Riesling before the last of its refrigerant found its way out to disrupt the ozone layer.
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