Draino used to be made out of lye, which would damage metal pipes and the rubber seals in pvc pipes with normal use. But that's kind of ancient history.

For the past few decades Draino has been made out of bleach. It will dissolve low density clogs, like hair, but isn't particularly effective against solid clogs caused by things like fat.

Its not particularly caustic, so there isn't much of a risk to the plumber's health if they're wearing gloves. But it will dissolve some of whatever was clogging the drain, which usually turns it into a sort of chlorinated poop water. The fact that there will still be some bleach in it also means that if it spills it can ruin/discolor the stuff that it spills onto. Both of which makes it more difficult to work with than just dirty water.

Basically, Draino works on the things that plumbers don't normally get called out for and doesn't work on the things that they do get called out for. If you use Draino on a tough clog, you haven't accomplished much other than to make the repair miserable for the plumber, who has to clean it up afterwards.