This isn't going to make Google any friends. I can see why they'd prefer it be a Google search box but we all have our favorites. And telling a blogger at blogspot what he can and cannot have on his blog is likely to lead to bloggers moving to other platforms, like Wordpress. I, personally, wouldn't tolerate that crap.
Another example of Google's arbitrary behavior. There was a time when Google's corporate ethos was do no evil. In the world of bloggers and blogging this is perilously close to evil.
What I don't understand is why so many people support Google, instinctively and uncritically. I've had enough run-ins with Google's arbitrary nature recently to really not like them.
But judging by this thread at Digg, most people love them.
Strange.
I will say this: I think a lot of net users are in for a rude awakening soon concerning Google.