I think the central question is why did he want them all dead?
Politicians evaluate things politically --I think that as things were Of High Moment that day after 5 pm Obama was pondering How Public all these events would become:
"Will there simply be a foreign policy failure? Or instead will a very major Arms Smuggling Scandal come to light, with hearings with stern Senators rattling papers in front of cameras, and witnesses telling heart-rending stories in excruciating detail....?"
"Will these 40 folks here in the field die, OR will there be a very major political scandal that lays low my whole Administration...?"
I don't think the President wished ILL upon any of those guys at all, but out of political expedience that night it really would have been best if they had all Gone Away --that is, if they all had died and could therefore not ever testify.
Same reason he wanted SEAL team six dead. He despises (and fears) the US military, especially the Special Ops folks.
https://en.wikipedia.org/wiki/2011_Chinook_shootdown_in_Afghanistan
To hide the FACT that we were selling GUNS to Syrian rebels, via Turkey. And .. a man from Turkey was meeting with Stevens on 9/11 (and I’ve often wondered if this was on purpose .. because the attack did not begin until after he left the compound).
Obama had told Putin that WE WERE NOT SENDING WEAPONS TO SYRIAN REBELS. Hmmmmm ..?? Another lie ..?? But, Putin had info that American weapons had been found on the Syrian battlefields.
And .. wanting to be rid of this “problem” .. might have been a very good reason to withhold signing the CBA.