Hey, Joseph -
Short answer? No. There is no supported way to achieve this using the CLI tools or the REST API. I'd guess the reason why you can't select a single View to be "everyone's" default start page is the designers don't want to put an Admin in a position to inadvertently assign a start page to users who might not have permissions on same. Have no idea what would happen in that situation, but suspect it wouldn't be good
That said, there is probably an unsupported way to do this....You'd make a change like this at your own risk, and modifying system tables directly puts your Tableau Server outside of support boundaries....if you break something, you're on your own: Game. Set. Match.
Anyhoo, there's a table called user_prefs in Tableau's metadata database. I just set my start page to something and peeked in this table:
Lo and behold, I can see the viz I just chose (Book1-WithTabs).
SO, if you know how to write UPDATE statements, can figure out WHICH rows need to be modified by examining other tables in this db, and can sleuth out way to connect with WRITE access to the db, you can probably come up with a workable solution...If you can't (please don't take this the wrong way) and need help, you're probably self-selecting yourself out of the group of folks who might consider actually trying this...