Those aren't my words, those are the actual words actually spoken onscreen by Picard in "Attached."
False. Picard's words, as already quoted, were "Every member of the Federation entered as a unified world, and that unity said something about them." Nothing about the form of government there. Indeed, Crusher responded with "By all indications, the Kes are a very unified, very progressive people.", suggesting that planetary government was only peripheral to the discussion. Picard accepts the response as such.
If a world is applying for membership in the Federation, it's already a given that the first contact protocols no longer apply.
...Or, more exactly, that they have already been dealt with. Meaning that compatibility with first contact is a requirement for membership in practice.
Although this sidesteps the issue that there can be many ways to qualify for first contact. Meeting Starfleet or UFP criteria is one of those. Just actively initiating first contact on one's own is another, whether Starfleet or the UFP likes it or not. Being forced into first contact by a third party is yet another.
Starfleet or the UFP can't always choose the terms of contact. They can dictate the terms of membership, though. But if contact was by the second or third method, then we cannot claim that the applicant has already met a set of criteria by the very act of applying. Unless the only set of relevance is "the ability to contact and apply", that is.