I've not dipped my toe into the Persona games, but many of my friends and colleagues love them. According to Atlus developer Kazuhisa Wada, that's a key and very intentional part of how the company makes the series.
Wada recently spoke at the CEDEC+KYUSHU developer conference in Japan (reported by Game Makers with translation provided by Automaton) about how the company's design philosophy has changed since making Persona 3 in 2006.
Before Persona 3, Atlus' values were coined as "Only One," by Wada. It basically meant, "if they like it, they like it, if they don’t, they don’t." Rather than making games with broad appeal that don't do much of anything so as not to potentially put anyone off, the Persona series does what it does very well: stylish action, dungeon crawling, and deep relationship development.
When I write it like that, I convince myself I should play. In some of the games even elements like time and the weather can affect fights and the story itself.
It all sounds cool, and I appreciate it from afar, but for some reason they've just never clicked with me. Based on the company's past values, that's just fine.