Beta readers are not explicitly proofreaders or editors, but can serve in that context. Elements highlighted by beta readers encompass things such as plot holes, problems with continuity, characterisation or believability; in fiction and non-fiction, the beta might also assist the author with fact-checking
It sounds like you are talking about copy editing. I think that's a standard part of publishing. Good copy editing should catch the type of things you mentioned. Things like inconsistencies, problems with timelines, overused cliches and themes, even changes in character personality.
One problem with doing it all yourself is that you are too close to it. In your mind you know what's supposed to happen and how it's meant to be read, but what the audience is reading might be something completely different. It's a case where someone can look over your shoulder and immediately see something obvious that you miss - because you read what it was supposed to say rather than what it really said.
are they necessary? no. can they help? definitely.
the thing is, that book is your baby; you're emotionally attached to it because you gave it life. but, let's face it, we ca all benefit from an unbiased "third eye"~ someone who isn't emotionally invested in the work and can constructively critique it for what it is.
i will definitely have beta readers when the time comes, and i've offered to be one for my writer friends, if they choose.
I wouldn't say necessary. I would say that it's extremely helpful, just like being part of a writing group can be extremely helpful. It's hard to criticize your own work, so without other people's input editing can be really difficult.