Can a freestanding bathtub drain be damaged by regular use?
There would be no such thing as "excessive wear" on a bathtub drain - unless there was caustic material being poured down the drain which ate away at the drain pipe and joints.....although from the sounds of it this is far from the case here.

For the sake of discussion let us assume that the tub is a quality name brand product.

It may be that there was excessive flex on the drain pipe joint to the tub, especially in the case of a plastic or fiberglass type of tub. Excessive flex would only be brought on by an improper installation of the tub where it was not supported in the correct manner or the drain pipe was improperly installed.