Generic own-occupation LTD certainly would. The own-occupation part is important, because without it most LTD policies only cover you if you can't work at all. Even then, quite a few generic LTD policies only covers own-occupation for a few years. Own-occupation to social security normal retirement age coverage is surprisingly expensive.
I would expect there to be quite a bit of moral hazard involved, therefore it would have to be expensive otherwise insurance companies would be taking a loss.
