I am at a loss as to why we are "abandoning" random variation, and I don't believe I can cut through this thicket of verbiage to get at it. But I am not quite ready to toss it in the trash bin, and I don't believe most biologists are, either.
We obviously have random variation to provide a base population upon which selection operates. We are recently noticing that our centuries-old assumption that the randomizer had a uniform initial distribution before selection started whittling on it, might have been off the mark.
There are probably a number of reasons, one is the possibility that what appears to be random might be law governed (cf. Wolfram's work on cellular automata), another is an observation made by a pro-Darwinian-mechanism-evolution FReeper in response to a query of mine ages ago: selection works at a cellular level, too. (Which opens the possibility that filtering cellularly lethal variation out of changes at the level of precursors to germ cells might produce some slight bias toward globally beneficial variation at the level of heritable changes.)
There is also the fact that the 'randomness' for all Dawkins confidence that it is randomness on the ontological level like Brownian motion or the collapse of the wave-function, was really always just epistemological randomness--we don't know a law governing pre-selection variation, and it's unpredictable to us.
It might also be a political move: admitting that it's epistemological randomness rather than "chance" takes a bit of the heat out of the debate.