My main question is why adaptation should be attempted and funded only for AGW, and not to address risks associated with the current climate and natural climate variability?
I would guess for reasons of predictibility and politics.
Presumably the purpose will be to establish some kind of risk metric, similar to flood-years currently used by local and state planners, and provide a risk-evolution timeline. Even under the considerable uncertainty of future scenario and climate sensitivity this is feasible in relation to anthropogenic changes but not so much for natural changes, which are currently unpredictable, or happening on timescales well beyond normal planning practice.
There’s also the element of political unwillingness to subsidise people who choose to live in locations which are inherently climatically vulnerable. If those areas carry economic advantages those can be used to pay for necessary defenses.