I like to subdivide data up into different geodatabases. Being able to create a new FGDB in the output dialog for a tool is a great help, but if you could toggle that new FGDB, or any other you have to be the default geodatabase for your project, that would make it even easier to quickly put data where you want it to go. I'd suggest just adding an extra option to the context menu for the FGDBs, the current one is shown in the screenshot below for reference.
I note @CarlMorrison's comment pointing out that you can do this, if you view the Databases section of the Catalog View\Pane, as shown in the screenshot below, but my failure to find that may support my request, or just say something about my abilities ;-). Being able to do this in the output dialog would, to my mind, be consistent and useful.