There were American forces all over that region - suited up and ready to go in... Someone had to stop that logical action from happening...
Of course, with events possibly being well coordinated, and reportedly an ambush already staged, a rescue mission might have been planned for by the adversaries to also ambush, ...setting up another Desert One,..this time for Obama instead of Carter.
Since the company sized assault lasted more than 15-30 minutes,..approaching 8 hours, the discipline of the adversarial force manifests it wasn’t world league. Nevertheless that is substantially more firepower than a fire team of civilian commandos.
My guess is the inaction was due to arrogance at the top, coupled with indecision and lack of insight, and refusal to accept courses of action prepared by those of lessor rank all in competition with a warm glass of Ovaltine and beddy-bye.