I thought the opposite, honestly. I was fully excited to play a new Persona game but thought it dragged on waaaay too long and had too many scenes where the characters reiterate the mission statement and core premise. I think a lot of it is that I think 5 has the weakest story/writing of this bunch by far, so it felt like they were really belaboring points I didn’t find especially compelling.
For all its faults, 3 states its thesis right up front with a bullet and executes on it well. It hits its marks well, and the music really highlights the emotional impact they’re going for. I haven’t played Persona 3 in…10 years maybe? but listening to any of Living With Determination, Memories of the School, Memories of the City, Memories of You, ohhh and that last boss track. They’ll just fuck me up for an hour. I’m getting chills just thinking about it.
4 can rely on its mystery trappings, and has more charming characters (though they are more limited by nature of their arcs being resolved almost immediately and through S-Links instead of through the narrative) . It’s no wonder that so many people like it, it hits the balance of gameplay, story, and fluff well and gives off the “hanging out with friends” vibe more than 3.
5 had the least interesting story and kind of failed to hit the highs it struck in the first palace for the rest of the game IMO. The characters are good, but I have fonder memories of the P4 gang. It’s very stylish and has good music but it’s mostly sizzle and not much fsteak. The mechanics are great, and why I’ll probably save it for last.
Don’t get me wrong, they’re all great outside of some unfortunate garbage and I will 100% them all yet again, but 4G comes the closest to making me excited about that prospect. That said I haven’t played P5R yet, so maybe I’ll be recanting when I get around to it 
Incidentally, the way I feel about Persona 3 is the reason I think The Answer is absolute garbage. Just totally craps over everything the story says and the characters accomplish. Terrible excuse for an epilogue.
Edit: Forgot about Heartful Cry, the only good thing to come out of The Answer. That track is awesome. Also, “with a bullet” up there was an unintentional joke.