@"which means it must be the local search capabilities that caught Google's eye"
I very much doubt thats their primary goal, although they would like that side of the product. (Local search is just a good smoke screen to use for their real goal).
I think what they really want is to make email on iPhone the same as gmail, in that Google then gets to read the emails. This remail looks ideal to pass email data via Google's vast server side spyware on its way to becoming email on iPhones. Then Google will be able to legitimately claim you can use Google search facilities on your emails on the iPhone, because Google has read your emails, which is what they really want.
Whats the betting the relaunch of the product (with much (as usual two faced) trumpeting from Google) will be accompanied by just such a new EULA change, to allow them to monitor the email accounts via their servers. Of course all the trumpeting of the search facilities is yet more Google Doublespeak for what they really want, which is access to ever more of peoples data.
After all Google's primary (doublespeak) goal is to organize the world's data, so now they can sort through and organize peoples iPhone emails. (As for the fact they read what they then sort, well that part will be down played as usual. Don't look at that part, trust us we are Google, look we say (in yet more doublespeak) that we will not do evil, so you can trust us.
Another day and the unstoppable Google Goliath rolls on (over as much of people's privacy as they can get their hands on and get away with). Amazing how much they are being allowed to get away with, which strongly suggests they have very powerful friends in governments. :(