Prior to moving to the UK I worked at a university and was responsible for assisting the international students. Basically everyone came to the US on a student visa, and then we had a European student who was issued what was essentially a green card. She didn't understand why, nor did we. We thought it had been issued in error. It turned out her mother was a former US citizen, and this student didn't know that. She knew her mother was born in the US, but didn't think she was ever a citizen. She also found out her maternal grandparents were US citizens and were still living in the US.
What we had found out was that her mother renounced her US citizenship prior to her birth. Long story short, her mother became a citizen of European country and cut her ties with her family in the US. This student said she felt a bit "betrayed" by her mother for doing this, as she had family she never knew about, as well as the visa hurdles. Families can be challenging, but from what this student said, it sounded like her mother just wanted to be "European." This was years ago and I'm not in touch with the student, but she was super keen to stay in the US and eventually apply for citizenship once eligible.
Slightly different to the situation above, but my friend born in the US to British parents found out when she had her first child that she was not eligible to pass on her US citizenship to her children. Even though she had no ties to the US other than it's where she was born, she was hoping her kids could have citizenship so that they could take advantage of any opportunities that came their way. She had left the US as a child and hadn't lived there since, so the issue was lack of US residency (the US Embassy's website has more info on this:
https://uk.usembassy.gov/u-s-citizen-services/birth/transition-requirements/). She and her family really enjoy holidays in Florida, so her kids get ESTAs, but it's a huge hassle when they arrive in the US because immigration want to know why the kids aren't travelling on US passports. She explains they aren't elligble and that she's tried to get them citizenship, but every single time they go to the US, immigration is really difficult with her. My friend's UK passport shows the US city where she was born, so if she had tried to enter the US on a UK passport, US immigration would question why she wasn't entering on a US passport and why her kids weren't either. I would think that for a former US citizen (who was born in the US) who was coming to the US for a holiday (for example) on their UK passport would probably receive quite a bit of questioning as to why they didn't have US passport. And if travelling with their children, there would be questions as to why the children don't have US passports. If it gets messy for my friend just going on holiday with her kids, I can only imagine it would be even messier for a former US citizen trying to visit on their UK passport.
I'll be applying for UK citizenship this year (just waiting on my ILR decision!), and I'm super excited about having dual citizenship. I don't have kids yet, but my UKC husband and I are very pleased that they'll have dual citizenship from birth. As adults, they'll be able to decide for themselves where they want to live and won't have to deal with the Home Office. Nobody wants to deal with the Home Office, and having the luxury to never deal with them is worth its weight in gold.
For anybody considering giving up US citizenship, I would really think about the pros and cons. Really reflect on it, and ask if this is a short-term solution to something (such as not wanting to file taxes), or is this something that may be very valuable long-term (ie: going back to the US to care for a sick relative at short-notice).