As mentioned, the gear was made of plastic/nylon as a failure point. If the specs of the gear a known (pitch, # of teeth and pressure angle) a new one can be made. Many folks are having success using 3D printers. Steel is fine too and as mentioned, a false center bushing held with a shear pin would be a good idea.
If the rest of the lathe is in working order and it serves your purposes, heck yes, just replace the gear.
As far as "abusing" a lathe. Abusing a lathe is when people take medium duty machines install chucks and toolpost holders that are 1 or 2 sizes too big and attempt to hog-off metal the same way Abom does with a 3 ton machine with a 15HP motor.
Crashing a piece of equipment is something to absolutely avoid at all cost. Doing it intentionally is a clear-cut case of abuse. That said, if anyone uses machines on a very regular basis, there are two kinds of machine operators... Those who have never crashed a machine -and those whose turn is coming.
Not all crashes are catastrophic and not all are avoidable. It's happened to me twice. Once when a a parting blade broke (out of the clear blue sky) and once when my oily hand slipped off the carriage release. My brake pedal cuts power and seizes the main spindle. Other than a bruised ego, no harm done.
Ray