For what it's worth, I recently discovered that I can move windows on GNOME by holding down the Windows/super key and dragging. It's a small thing but it's actually quite nice.

This is one of my pet peeves, too. I shouldn't have to find some pixels of unused space on a title bar before clicking on it lest I bring down another menu or launch something. Microsoft programs seem to be enamored with the "search input box in the title bar" concept. Give me a magnifying glass, and drop down the input box or something. I want to be able to just grab the title bar and move the window.

For me, what you're referring to is one of the reasons I don't like to use Windows as a desktop OS (because you need to hunt for these relatively small target areas to organise multiple windows). The alternative which I greatly prefer is outlined in the other responses.

In the past, I used to disable title bars entirely even on full-sized monitors. These days it's not so easy to do that, though.

You can grab any part of the headerbar to move the window - even buttons and other widgets. It won't trigger them, it will just move the window.