The way I remember this is that verbs which have to do with variants on "being" (of which "becoming" is one) behave like "esti" in not using the accusative.

• I want to become a nurse ~= I want, at some time, to be a nurse
• mi volas fariĝi flegisto ~= mi volas iam esti flegisto

The examples in https://en.wikipedia.org/wiki/Esperanto_grammar#Nouns_and_adjectives are also relevant:

• mi farbis la pordon ruĝan (I painted the red door)
• mi farbis la pordon ruĝa (I painted the door red).

I try to hear the second one as something like "I painted the door to be red" and that reminds me the accusative doesn't happen there.

Ŝajnas ke verboj kiuj enhavas “-iĝi” ne bezonas la “-n”.

The root is "flegi", which means "to nurse" or "to take care of". It comes from the German word "pflegen" which means the same thing. https://en.wiktionary.org/wiki/flegi

Akceptendas, sed laux kelkaj (ekzemple Jordan) gxi ne preferindas.

Estas nun akceptita.