I can never over look how unwelcome female gamers often feel, and I can't really deny that Princess Peach plays a large role in why they're unwelcome. However, Princess Peach doesn't bug me.
Why? Well first off let's start off with her often being a damsel. At this point it's clearly kind of joke to the Mario game creators. They come up with some reason that Princess Peach is kidnapped and then Mario has to go through the levels to save Princess Peach. With the exception of Super Mario Bros 2 which kind of wasn't really Mario game in some senses. Mario games have a very set storyline and it's extremely simple. Arguably if you changed one of the really major factors in such a simple story it wouldn't be a Mario game anymore.
On top of that Princess Peach is playable character in the RPG Mario Series, along with the Paper Mario Series. She still sometimes needs to be rescued depending on the specific game, but she has her own powers and abilities to aid in the story.
That's not why she doesn't bug me though. The reason she doesn't bug me is cause she's a representation of a type of girl. I knew girls who loved her game, they loved that it was pink and girly, and they loved that her crying and her rage was a strength. In current society women are presented as overly emotional and it's seen and detriment. I knew girls who felt empowered by Super Princess Peach.
The problem isn't that Princess Peach exists in my opinion. The problem is that she's so all encompassing because video game creators do not seem particularly interested in created other female video game characters. We need female video game characters that are as varied as the male characters. Honestly until that happens, female will probably continue to feel unwelcome in the world of video games. I vote we stop sending all the hate to Princess Peach because that can make other female gamers feel unwelcome and send it where it's deserved. At the actual game creators.