Hi,
according to entire discussion, in the [0], it seemed the problem was not the tree structure, but rather the inability of the tree based navigation to remember its last state, after the query. So if we can fix that, i think the problem will be solved.
However as the adam suggested, we can have that "Most often used Database" feature. Along with that we can also provide the sorting of the database on the basis of their creation time(so the most recently created database will always be on the top). I guess providing these kind of options will definitely help the help the user, but reverting back to old dropdown database selection will not be a good idea.
[0] https://sourceforge.net/p/phpmyadmin/discussion/Help/thread/ae8b9e05/