>>63856293 (OP)Unironically inter-service fuckery
In 2011, JSOC had the Middle East divided into two areas of responsibility for special mission units. Delta Force was responsible for running most missions in Iraq, SEAL Team Six was responsible for Afghanistan. Since the mission was launched out of Afghanistan, the SEALs got the mission.
It probably didn't help that Delta Force had completely botched the first attempts to get bin Laden in 2001 either.
>RangersIIRC Rangers were held in reserve just across the border in case the Pakistani police or military responded (spoiler: they took one look at the shootout and kept on driving), on raids like this, Rangers are usually used as a blocking force or held in reserve so it's not uncommon.
>Green BeretsDirect Action is not the primary mission of the Green Berets, working with local forces is. Delta Force was originally created as a spin-off of the Green Berets for this purpose.
Personally I think they should have given the mission to MARSOC just so Osama could've been shot by some cheeky fuckers wearing M81 Woodland camo (they even could have taken his M65 Woodland field jacket as a souvenir)