But dying and being reborn is as bad as dying for the Chosen. I'm sure that the DO takes death as failure - for everyone but Ishamael, as his true believer and Anti-Dragon workhorse. None of them wanted to die and come back, none of them would risk the DO not getting them in time, and none of them would want to "owe one" to their dark master.
As for Asmo, his plan was to work with Lanfear to get Rand on their side, then train him in saidin. From the start, Rand was talking to him about duty and killing Shaitan. Also, Lanfear is ruthless and obsessed with Rand, so it would be really smart to assume that she'd turn on Asmo. Our Unholy Salieri should've seen that leaving the caravan would be wise. He tried to dig for info about Rhuidean, but should've split...