Overall I liked Beverly but I have to agree she had plenty of moments where I wanted to just haul off and smack her and would wonder why she was in Starfleet.
Like it or not the "idea" is that in 24c humans are no longer petty, self-serving and are out there exploring the galaxy for the betterment of mankind and on a quest for knowledge. They also have some deal of experience in the "messing with other cultures" thing and know not do it. The idea is supposed to be a Starfleet officer would sooner lay down his/her life than to violated the Prime Directive.
Beverly apparently missed that day of class because she seems to be all about violating the Prime Directive more so than Kirk or Picard ever are. At least when THEY do it it's not without a lot of heavy thinking and soul-searching.
Take "Who Watches the Watchers" for example. In this episode the Away Team are in a duck-blind watching over a Bronze Age level of development group of proto-Vulcans. The duck-blind is damaged in the process of fixing it one of the proto-Vulcans accidentally gets electrocuted and falls off a rock-face. Like it or not in this situation the reaction should be to do nothing. In the long run the society of the planet would be better served by the man dying from his injuries. Instead Beverly goes down and administers some hypo-spray triage and then beams him up to the ship for more intensive medical care. This is just plain reckless and, of course, in the process the guy sees the futuristic sickbay, a memory-wipe doesn't take and he ends up back on the planet wanting to start a theology centered around Picard and the Enterprise believing he had died and been brought back to life by supreme beings. This of course causes a disaster that ends up with Picard having to expose himself and the ship to even more people and eventually the whole tribe.
Again, all because Beverly missed the day in school that talked about the Prime Directive.
In "Justice" she hand wrings and frets a LOT over Wesley's "death sentence" (which, granted, she's justified a bit) and questions the entire culture of a planet. In "When the Bough Breaks" she, again, damns and questions an entire planet's society all because her teenage son was kidnapped by them. She really did seem to get fretty and kind of a superiority complex going with her a lot.
My biggest "Jesus, what is WRONG WITH YOU?!" moment comes in "Evolution." The first episode of the third season where Beverly has returned to the ship after a year-long absence. At this point Wesley is an acting officer on the ship.
She actually seems to HARASSS her poor son over him doing his duty and job! She pages him when he's not in his quarters, frets over him taking on too much responsibility and wonders why he's not "acting more his age." And when he DOES "act his age" and dates a young woman she takes concern over her 16 or 17 year old son being with a girl taking a "keen interest" in him.
Jesus. Christ! Really?! Beverly? Your son is an older teenager I'm guessing it's sort of okay in your society for a girl his age to hold his hand and show interest in him. Cut the damn cord!
off?! Wow, she doesn't fool around.