Yes, I can see the list of recent files. I would like it to open the most recent file automagically. I don't see an option for this in TextEdit > Preferences.
TextEdit will automatically re-open any documents that were open when you Quit it. (Assuming that this option in System Settings > Desktop & Dock is OFF, as shown.)
If you close a document, then TextEdit won't re-open it, unless you ask it to.
So if you want to keep working on it, don't close the document: just quit TextEdit.
I dare say it's possible to craft some sort of script that would query the list of recent files and open the first one -- but triggering that script is going to be at least as much effort as selecting the file from the list yourself.
To sum up: No.