Former Googler here: After an epic blind allocation fail, my attempt to switch to a project that made use of my talents enraged my manager and he reported me to HR. I left for greener pastures shortly thereafter and HR has apparently banned me from ever returning now that there is relevant work for me.
Obviously I have no knowledge of the specifics of your situation, but when I worked at Google I freely moved projects many times without a problem, my first time about 3 months after I arrived. I haven't worked there for a while, but I have many friends there and they change projects with some regularity.
If you're a new college grad or just new to the industry, Google rocks. But, if you have "a very particular set of skills. Skills I^Hyou have acquired over a very long career" then Google will most likely arbitrarily assign you* to whatever arbitrary team needs seatwarmers at the moment. And FWIW, my skills were considered irrelevant to Google the year I joined, but suddenly very relevant barely a year after I left.
*Unless you're an acqui-hire, and then Google once again rocks because you get both the perks and the interesting work.
