Probably much more important than chivalry: you can't ransom off a captive who is dead.

Ransoms were really, really large in that period. Five years after this battle, the English captured the French king at Poitiers. His ransom was 4 million gold coins plus, I think, various concessions. The French ended up having to pay a lot of ransoms through the whole war, and as a result, the nobility and crown were so poor they couldn't prevent banditry and famines.

Barbara Tuchman's A Distant Mirror: The Calamitous 14th Century is a very engaging account of this period.