The more I look into it the more I start to feel like it's entirely intentional. As OP mentions, the other forms of polymorph explicitly spell out you get to choose, but normal polymorph does not.

Also, while it's of course not directly related to DnD, there are some older dungeon crawling media that have both been inspired by DnD and been an inspiration to it that run with this interpretation. For example, in Nethack, a dungeon crawling game first released in 1987, polymorph is entirely random making it a gamble. At least DnD 5e caps the challenge rating so at worst you'd get another monster in the same ballpark strength as you had initially, in Nethack you could just as easily turn a goblin into a dragon.