You do make sense, but the answer is no. They zoom independently.
Because Premier allows you to look select clips for review in the Effect editor that may not be at the location of the cursor on the main sequence timeline I can see why it wouldn't be helpful for the two timelines to be synchronised by default but it would be useful if it could be enabled for those of us who like working that way. I am forever adding effects to the wrong clip.
My biggest problem is that with some clips, when I try to zoom in on the effect timeline I cannot get it to zoom in completely to give me the ability to move keyframes a frame at a time easily. Sometimes it'll let me zoom in to the max, other times it won't... it's very frustrating.
I admitted defeat earlier and asked one of the online advisers to look at it for me. They couldn't make it work on some projects either.
As Jim said, there's no way to link the zoom level of Effect Controls panel and the Timeline. And you're right that zooming via the horizontal scroll thumb can be clumsy, losing the playhead. However, if you zoom in/out via the +/- keys, voila! The playhead remains centered.
As for not being able to zoom all the way in, I've never run into that problem. If you can fill any details about the cases when it will not zoom in fully for you, I'd be interested. Regardless, one thing you could try is switching the Effect Controls panel to Show Audio Time Units. In that mode, you can zoom in much farther.