I really dislike how they're handled most of the time. Tears of Themis was probably the first mobile (gacha) otome game I invested a lot of time in, but I had to quit after maybe a year because my phone couldn't handle the storage requirements. I did try to come back to it on an emulator, but even then it just didn't work

Similarly, I tried Love and Deepspace, played for maybe 2 months, and dipped because grinding for currency in that game was pretty much impossible. Now that so much time has passed, even though I'd love to come back to TOT, I don't think I could enjoy it knowing how much content I've missed and will probably never be able to catch up on without spending money.
I'm sure there are plenty of mobile otome games that don't require you to spend money and don't have gacha elements, but I'd rather invest my time in titles that guarantee I'll get the whole experience while spending way less time on them.
Yumekuro was the one exception for me. I got really invested in it, and even after taking a break (because I lost my account and later recovered it thanks to their amazing support), I was able to come back and unlock every single character and story I wanted to read. It was definitely a time investment, but I don't regret it in the slightest. There were around 100 playable (capturable?) characters, and even though I mainly focused on my favorites, there were still so, so many other stories I could unlock just for the sake of it.
The sheer care and love put into that game was amazing, too. Every single story was voiced, including event stories, which were often an hour or two long. It's a shame it only lasted 2.5 years, and maybe not all of the characters were explored to their full potential, but thanks to the crowdfunding support, they were at least able to finish the whole main story. It's still available for free if you download the whole game, and the enormous amount of event stories released over the years is there too. Unfortunately, I lost the data I'd downloaded for my account, so I can't even go back and read everything I gathered during my time playing it. Though thankfully, I screen-recorded all of my favorite character's stories, so at least I'll never lose the 40GB of his content lol.
I honestly don't think I'll ever get this attached to another mobile game. It was an amazing experience.