ok, i will take a shot at answering the question as it was asked.
this anarchist thinks the concept of "poverty" is a purely economic one. and i want no part of economic systems. it is economic systems (particularly capitalism) that have so ubiquitously defined what "basic needs" are - hence the list enumerated in the original question (which i find hugely problematic).
individuals have widely varying "basic needs", even outside the context of economics and public relations (ads/marketing). people are different, with different desires, different skills, different priorities, different levels of comprehension about what it means to live without institutional authority.
if one lets go of ideas like security, equality, fairness, justice... (which are rooted in dogmas that i want gone from my world), then you are left with the opportunity for a liberated life as a unique individual with unmediated, fully voluntary relationships. as dot mentioned, nothing about that is utopian; folks still need to figure shit out, including how to meet their basic needs. nobody - or very, very few - will be able to do it on purely their own. hence, relationships. authentic, individual-to-individual, reciprocal, trusting relationships. imagine that!
if the answer being requested is one that systemically eliminates human suffering (due to hunger, illness, etc), then you are asking for another system; or at minimum, a prescriptive program. this anarchist wants no part of any of that. saving the world is simply not on my agenda; and in the world i would love to live in, that concept would be as meaningless as "industry".
let the systems and institutions fall, and let the individuals that remain figure it out for themselves. yes, there will still be human suffering and death. no big difference (from the current world) there. but here's a choice that i wish everyone had: live in a world where institutions protect and provide (and destroy and lie and ...); or live in a world where individuals - and their relations - do that for themselves.