I actually had a difficult time coming up with answers for this one. The male version of this thread was so easy by comparison. I think part of the reason is that there are a lot fewer anime that center around a female protagonist than male and many that do are shoujo romance where the protagonist is mostly inoffensive/uninteresting. I could think of more if we are talking manga where there is just a larger volume and variety of shoujo and josei stories.

I was able to think of a couple that I wasn’t a huge fan of when I was browsing the female protagonist tag on AniList.

• Usagi Tsukino - Sailor Moon - Look, as an older guy, I am not afraid to say I actually like Sailor Moon the show and have seen most of the original series as well as the Crystal remake. However, Usagi can be a not-great protag a lot of the time. She is just insufferably stupid a lot of the time.
• Kagome HIgurashi - Inuyasha - I think my gripes with Kagome really stem to Inuyasha being a bit of a dated show at this point. She is all too often either scolding Inuyasha or being a damsel in distress waiting for him to rescue her. If Kaoru from Kenshin were the protagonist, she would have these same complaints from me.
• Ai Tanabe - Planetes - This one was a big letdown for me because I love so much of this show, and I loved her character for most of it, but the ending of her character’s story in that show is just terrible and I hate it.
• Miyo Saimori - My Happy Marriage - A more recent example. I really liked the first half of this show, but as it went on I felt like it was just a whole lot of wasted potential.