The B.A or A.B. is not a job ticket. There are few jobs specifically for 4-year graduates, except possibly engineering jobs. If formal education is continued, it is usually followed by some kind of post-grad education, which is where the professional 'jobs' begin. Business management, lawyer, some medical positions, economists, those kinds of things begin to open at the masters level.
To write your own ticket in the world you might want the Ph.D. or other doctoral level degree. You have that, you are professional, end of story--it's up to you and only you after the doctorate: you have the key to the world in your hand. If you have some public speaking talent you might even run for high public office.
Not so for BS in engineering. A PhD candidate in mechanical engineering at my alma mater wrote his dissertation on processes we had commercialized (internally) years earlier. I make more dough than the tenured professors I know here in Houston. I'm far better equipped to teach in my subject than the PhDs because while we're relatively equal in terms of mathematics and modeling, I've had to make it work in the real world as opposed to writing esoteric papers about it based on observation.
An example would be the how and why of switching pulse streams to a stepper motor at speeds above the base speed. And I'm a gear-head (mechanical engineer).
Engineering is a field where an advanced degree is not nearly as necessary to be a "professional".
But I'll bet that's not true of a BS or BA in Astronomy...or many other sciences, let alone Art History.