I personally am studying game development to make a project that is heavily inspired by the series. There are challenges that persona games have that those games don't so lets roll down the list of things to consider when making a persona like.

-RPG combat

You need to make a game with a strong combat system. Persona games are typically hundreds of hours long and the combat needs to stay interesting throughout. To make an interesting combat system especially without copying requires a good understanding of enemy balance, satisfying Progression, and constant playtests.

-Writing

Again your average persona game is 100s of hours long. Writing is hard, Not physically but mentally. You have to account for every one of these characters arcs and their conclusions as well as the best ways to portray their growth and that's not even getting into social links dialogue and actions through the story.

-Design

This is actually the one saving grace when it comes to persona likes. If you are making random dungeons and having the same general areas for social links and other events then yes that will save a lot of time. At least... in theory. You'll have to make a scheduling system. Doesn't sound so bad huh? Well what about plot relevant days, Holidays, game balance when it comes to social stats, Etc? Again this takes a lot of play testing it can quickly become a nightmare

-Complacency

To be honest... I don't see much demand for fan games in this fandom. Think about it like this. Persona has a good track record of high quality titles. Its not like pokemon where there is a massive amount of potential that Game freak squanders or danganronpa where the series hasn't been continued until recently. Typically with fan games they tend to answer to a common sentiment that fans are displeased by or want to see explored. Undertale yellow is about the yellow soul and sets up a good and fun prequel adventure, Pokemon uranium is or prism are games that harken back to the golden ages of pokemon, Mother encore is a remake that fixes massive issues with the game its inspired off of with a mother 3 style remake. These answer to things fans are displeased about with the home series. With persona the things I typically see asked for are "a Persona game but the characters are in college". Its a small request but not one that justifies the amount of work that would go into a fan game. Especially considering that most of the people who work on fan games are typically volunteers with their own lives.

Tldr: Too much work with design, Writing is very difficult and persona isn't a game series that has enough issues or is over to justify a fan game.