A lot of TNG episodes would have been shorter if she had Troi's job.
Picard: "These fishy-looking ambassadors arrived in hibernation."
Lwaxana: "They're not ambassadors, they're terrorists. They have a bomb."
Picard: "Thanks, L"
It honestly would have made more sense if Deanna Troi was a member of the diplomatic service instead of being the ship's counselor.
It doesn't make sense having the ship's counselor do bridge duty when their time is best spent treating patients, but it does make sense having someone assist the captain by knowing the various treaties and international relations going on.
We just watched that one last night after a week and a half of dealing with heavy shit that still isn't done yet. Not really the episode I would have chosen to dip the toes back in after trauma, but that's what was up next. Still a great ep.
On my very first watch of TNG, I was so annoyed the first couple of times I saw Lwaxana or Q dominate an episode, but by the end of the series I was cheering every time they showed up!
I interpret her interactions with Picard a little differently. He might think she's a real pain in the ass, but I don't think she's actually being a sex pest, because they both know she knows there's nothing there. He's not going to be pressured into doing anything he's not interested in, which is something she also knows, and they live in a world where that's not OK anyway. It's a game, and honestly, an extremely gifted and perceptive telepath could cause him any number of problems. This is a man whose experience with people being in his mind was from the Borg. She's certainly found a way to come off as extremely harmless.
Partially negated by her telepathy. Theoretically she can ignore social boundaries in favour of going by someone's actual individual boundaries and hidden feelings/comfort levels.