The United Federation of Planets is a loosely conceptualized fictional government or political body wherein any aspect of its organization and structure is subject to the needs of whatever storyline it's featured in. Thus, few specific accounts of how it actually functions can be derived.
Given this diffuse presentation it becomes easy for two people to see entirely different things when looking at it and trying to explain it to others. What the Federation is largely becomes a function of one's own personal bias and imagination. It's the profound idea of the UFP, rather than the mundane liturgy of its function, that underpins its depiction. Thus, ancillary concerns such as its voting system, economic structure and minutia concerning new members never rises to the level of importance necessary to be included in the narrative, unless said minutia is specifically relevant.
There is no bible concerning how the Federation works, thus there are no right or wrong answers. There could be dozens more prerequisites for becoming a member other than those (seemingly) stated. Or there could be none. It could be like the UN, where once the very minimal standards are met, you're in. Or more like the EU, wherein the existing membership only lets you in if it's politically expedient.
Hell, every applicant may be required to have a recipe for fried chicken to even have their application considered. Or be a nice vacation destination (as so many seem to be). Or have heard of ABBA. We know they have to be able to quote Shakespeare and/or Surak, at the very least.
Or it could be absolutely none of those things. Until we get a West Wing style series specifically about the UFP, I doubt we'll ever know. But we can guess our asses off.