There are many words, phrases and sentences that are incorrect but somehow become popular through generations, so popular that the correction sounds incorrect!
Preponderance of errors can make them seem right.
Just one example: Using PBUH (peace be upon him) after the name of Prophet Muhammad is most obviously wrong. Does he need our prayers for peace? Of course, he is in peace. But the error has been perpetrated by even the highly educated Muslims for centuries.
I have been recommending to use "the exalted Prophet", "Muhammad (S)" or "salutes to him". Only some families have taken the advice.
Since "Assalamu Alaykum" has been in practice universally for centuries, it might be very difficult to bring the masses to make a change. However, I will continue to work on it.
Further input from friends will be appreciated.
A lifelong student