Multiple modes of interaction -- a verb menu -- might not make any individual puzzle more difficult, but having those kinds of options adds to the overall complexity of a game. The more ways to interact you have, the less likely you are to stumble on solutions rather than arriving at them with forethought.
Of course designers need to build puzzles that take advantage of less-than-obvious combinations of interactions and use them sparingly so they remain less-than-obvious, but I guess designers don't want to do that these days. Imagine Bernard walking into the surveillance room in the mansion, clicking on Edna and just pushing her, without giving the player an opportunity to talk to her first, and maybe not even trying to push her until they realized why they might have reason to.
I've never thought of the verb menu or verb icons as "the interface". I think of them as my character's abilities, in the same way a shooter has combat capabilities or a character in a platformer has various ambulatory abilities. Designers of those kinds of games are constantly looking for ways to give players more options, but we adventure gamers are stuck with one click and watch the character do what needs to be done.