About Ser Jaime charging Drogon and Danaerys with his lance at the end, Wikipedia says this:
Coster-Waldau also stated about his character, "Jaime is such an idiot that he thinks for a second, 'If I can do this, I can win the whole thing in a 'Hail Mary.'"
Personally, I think this hearkens back to Season 1 where Robert Baratheon was discussing “War Stories” with Ser Barristan Selmy and Jaime. Apparently, the first man Robert ever killed was at the Battle of Summerhall.
“Some Tarly boy. Came running at me, thinking he could end the rebellion with a single swing of his sword. I knocked him down with the hammer. Gods, I was strong then! Probably shattered every rib he had. Just before I brought the hammer down he shouted, “Wait! Wait!” Hmmppfff! They don’t tell you how they all $#!+ themselves when they die. They leave that part out of the songs.”
Note also that an earlier conversation in the latest episode, between Jaime, Bronn and Dickon Tarly, covered the same aspect of battle. Dickon remarked that battle smelled worse than he expected. Bron remarked: “You mean all the $#!+? They leave that part out of the songs, don’t they?” (or something like that).
And there, at the end, is Ser Jaime trying to win the whole thing with single thrust of his lance. Didn’t work out that time either.
“hearkens back to Season 1”
Agreed - Arya & Sansa in the crypt at their father’s grave commenting on the poor likeness of the carving: “everyone who knew him was dead”
I think it’s simpler than that. Jamie is too proud to run. He’s not going to abandon his men. He’s going to die fighting. He sees Danaerys within reach. So ....