No law keeps President Trump from selecting a nominee that’s not already on his list, so as to keep the Democrats from ambushing the next nominee.
I dunno, the opposition research machine that the Democrats have running in their basement can ramp up an awful lot in a matter of hours, once they get a name, so not already being on the list may not be all that much of an advantage.
Amy Coney Barrett may be the next on the list, when RBG finally gets good and buried. And she could be there for at least as long as a successful Brett Kavanaugh.
That the list is so heavily vetted already is a big part of what gives the Democrats fits.
They can’t impugn the selection process, because the process was conducted in secret before Trump’s primary campaign began and their surveillance network was not yet tight enough to watch it happen.
Stick with the ones he has, they are likely all chaste monogamous judges selected to survive the sort of grilling we just saw. Trump knew their playbook.