Rampant capitalism is kinda genre-defining for Cyberpunk so Cyberpunk without corporations wouldn't really be Cyberpunk. _The Matrix_ only qualifies as Cyberpunk because within the matrix the machines effectively control the capitalist power structures to exert their influence.
Abundance/scarcity isn't really about availability, it's more about access. You can have a cyberpunk story in a "post-scarcity" setting in the sense of availability (due to sci-fi tech) but you can't have it without unequal access to those resources.
Agreed, which is why The Culture (series) isn't cyberpunk but The Polity (by Neal Asher) kinda skirts the line, in many ways they are similar except resource inequality still exists on a wide/policy scale in the latter.
Right: I'm implying that the genre definition itself places an upper-bound on how impactful AI is "allowed" to be, which creates a kind of (heh) no-so-anthropic principle, ex:
A: "Why isn't there more AI in cyberpunk media?"
B: "There's a decent amount already, as characters or tools."
A: "But why didn't those authors address its potential to be even bigger?"
B: "Some did, but that makes stories we don't categorize as cyberpunk."