I'll add your vote for a default track height preference.
Note that track height is saved in the project, but if you have already saved a project, changing track height does not force a project re-save; in that case you would have to make some edit before changing the track height to save the new track height in the project.
Or how about:
- launch Audacity
- Tracks > Add New > Audio Track (assuming you work in mono)
- Drag the track height as you want it
- Save the empty track as a project for example "empty.aup" (no quotes)
- Place a shortcut to that AUP file on your desktop. Use that shortcut to launch Audacity then SHIFT + R to append record into the empty track.
- If you save projects, don't save them with the "empty.aup" name.