We don't have morticians in England. Here we have undertakers (which I admit is a euphemism both bland and unhelpful) or we have funeral directors - which is not a euphemism, nor bland, nor unhelpful.
Still, a lot of my problem with the word mortician is that I am much more familiar with Morticia:
Carolyn Jones as Morticia Addams in the 1960s TV series
than morticians, and though Morticia is a admirable woman in many ways she's not the sort of person to whom I would happily entrust the corpse of a loved one.
Mind you, it's not always loved-ones we end up having to bury.
Now, there must be very many morticians who don't look as if they've just slid out of a crypt, but some job-description less dramatic, less necrophiliac, would be reassuring.
Things are bad enough as they are, after all, without worrying about the person in charge might be looking to whip up custom.
Word Not To Use Today: mortician. This is mostly an American word which was made up in the 1900s. It's basically the beginning of the word mortuary with -cian tacked on the end, as in the word physician.
Unfortunately, because of the way the word has been carved up, it rather suggests that, as a physician brings physick, a musician music, and an optician optics, a mortician brings death.