Biological warfare is less effective once the transport networks are down. Bioweapons need to be used as a covert first-strike option to be fully effective, and it lacks the instantaneous targetable effect of nukes.
And the human resistance wouldn't need to be eliminated to achieve robot world domination, let the humans enertain a hope and idea of a human future while keeping them suppressed and holed up in some backwater countryside while disseminating and expanding industrial capacity in places they can't reach to ensure that anything the humans destroy can be replaced with tenfold redundancy, after a century or so when they've expended all their advanced weaponry and industrial products, dig a moat and fill it with radioactive waste to keep them contained and see as they regress to pre-industrial society, at which point the robot relief effort can roll in and do some history revision to ensure that the following generations grow up to believe the humans destroyed themself in a greedy war, and now the valiant robots have come to rescue the remnants of mankind(and making them servants of the machines in the process)