"Accessory units are usually rented, while live-work units are typically purchased...."
One provides the community with affordable rentals; the other supports entrepreneurship and self-reliant, income generating citizens. Both create a source of income for the owner. Yet in Honolulu, these activities seem to be discouraged.
I say this based on recent revisions to the Land Use Ordinance that restrict the max floor area of new home-based businesses (i suppose pre-existing ones would be considered nonconforming) and the limited and onerous requirements to create a legal second unit.
But there is a growing (based on 1980's and earlier) body of research that suggests that other cities realize the benefits and actively work to incorporate these uses into their urban fabric. Here's a link describing Ontario, Canada's 2011 changes to allow Second Units: http://www.mah.gov.on.ca/Page9575.aspx