Inconsistency of all formal systems that include N (natural numbers set) from a not-finitist point of view

Considering the set of natural numbers N, then in the context of Peano axioms, we find a fundamental contradiction from a not-finitist point of view. This proof of inconsistency is not finitist because it requires to consider an infinite totality. But can we really summarize the finitist point of view as follows? ”A list of infinity elements cannot be considered for deducing, although it has to exist in agreement with the axiom of infinity”. Is this not an acceptable point of view and then are these not finitist proofs of inconsistency valid in a general way?