Nope. It is 100% the passenger's responsibility to possess all required documents for every segment of the ticket flown. Period.
The sole reason that air carrier's check documents is to protect themselves from being fined and stuck with passengers at transit and arrival points when passengers arrive without valid documents. Carriers do not check documents to help out passengers.
IATA's TIMATIC database can be accessed without cost from a number of locations including:
https://www.united.com/web/en-US/app...aspx?i=TIMATIC
but that would not have helped OP here. He obtained a single use Schengen visa and then attempted a second entry.
The best solution is to either pay a great deal of attention to detail or to pay a good travel attention who books a lot of complex international itineraries. OP is extremely lucky that his carrier helped him out. Many would have simply left him to fend for himself.