As a followup, my terminal windows are rarely the same size as my browser windows. I don't like resizing my browser windows in general because the browser will remember the new size, even though it was meant as a once-off window. So having a browser-sized terminal doesn't seem like a very good experience.
Additionally, it doesn't even work right. In a screen-controlling app like vim it seems fine, but in the normal shell, once I enter enough text to use more than a screen, the bottom-most line is actually off the window (even if I scroll down).
The missing lines at the bottom is a bug that got fixed just after this release. The next Secure Shell release won't have the issue.
And your browser size issue goes away if you open the terminal in its own window. Chrome even has an "Open as Window" option (right click on the Secure Shell icon) to open in a window with no browser UI.
Additionally, it doesn't even work right. In a screen-controlling app like vim it seems fine, but in the normal shell, once I enter enough text to use more than a screen, the bottom-most line is actually off the window (even if I scroll down).