[notpushkin]

You have to take your hand to mouse, do 4 clicks, then go back to keyboard. Not the end of the world, but it's annoying and is bad for people with. e. g. RSI.

And to remind users about date layout, you can just put MM/YYYY or MM/YY as a placeholder. Of course, if you care about your users and want to go above and beyond, you can even support both MM/YY and MM/YYYY – it's not that hard!