Doctors charge from start to finish.
Lawyers charge from start to finish.
Golf pros charge from start to finish.
They are considered professionals. But none of them sign your logbook or have to abide by the avalanche of rules that FAA certificated people do.
If instructors are supposed to be professionals, then they need to deliver good value and charge accordingly. Which means posting your rates up front, so no one is surprised.
Signing off someone for solo, and then leaving before they are done, is unwise at best. Rushing off to a "real job" means the instructor doesn't take himself or his client seriously, and that is a grave error. When I am with a client, that job IS my "real job", no matter what else is going on in the background. It would be impossible to defend your certificate if something happened, no matter how small, such as the client striking a taxi light on his way back to the ramp. Careless and reckless is a favorite charge of the FAA, and a CFI gets a 90 day suspension, minimum.
Yes, the client is on the instructor's ticket until he gets his next BFR. Or next rating. If anything happens before, the FAA goes after the last CFI to sign his log book. So you are on the hook for up to two years at a time, both in the FAA's eyes, and in a civil court room.