It certainly didn't happen that way for me. I'm doing exactly the kind of work that I love to do. You're afforded quite a bit of mobility inside the company.
If I am in Gmail, it pops up the menu (but at the bottom, and not where the hamburger is). Chrome pops the menu up. Maps opens the side bar. YouTube pops the menu up. Drive opens the menu.
So it works for some but not for others. Perhaps you could enforce consistency or follow your own guidelines etc.? Go crack the whip.
And I guess they think that the three dot menu is ugly or something.
I'm a new hire, and I've been given the choice of working on one of two teams, neither of which particularly align with my interests.