It's a shorthand in common parlance, and not every group needs to be monophyletic to be useful.

Maybe. But this one isn't imo. How can it be useful to call snakes, birds, crocodiles and pterosaurs "reptile"? It makes no sense. At least if you exclude avemetatarsalia it says something about scaly skin and stuff, but that's not the common parlance use so in my opinion it's better to just throw the entire word in the bin :)