Both PSP Dissidia games, hands-down, no contest.
Final Fantasy Dissidia Duodecim complements a lengthy story mode with a fully featured suite of RPG progression systems, shops, unlocks, challenges and extra modes. It's the kind of experience where you could actually sell the game JUST on the merits of its solo content.
In fact, I bought both Dissidia games without any intention of ever playing multiplayer.
This. Structurally speaking, Dissidia was great - the full story was completed by playing through each character's path, which reflected at least part of the story arcs of their respective games, and all of them had a difficlty setting assigned to them, and since the devs expected people to start with popular characters/games, Cloud and Cecil had the easier chapters to people could jump ahead and start with them.
Since you unlocked weapons during story modes too, stuff you unlocked for a character could then be applied to another character when you played through their story mode, which made to a nice progression curve.
The other neat thing is practically all of those character stories happen in parallel, yet with some degree of sequence, and the game's Theater mode then lets you watch all even in their canonical chronological order after you play through them. Another nice touch is that Warrior of Light, as the OG protagonist, not only had the highest difficulty assigned to him, his story start before and ended after everyone else's.
And or course, after you were done with all of that, there was still way more to do, also with some story assigned to it.
The other game with a very good single-player mode is Dead or Alive 5 - its story mode doubles as a tutorial, has you play through several characters, but unlike MK9 and its ilk, the moments in time where their fights take place, while sequential, are momentarily depicted only for the moments that matter those characters, with the implication made clearer as you advance through more character chapters, that more stuff happens in-between - progressing in the story mode makes a chronological map of events clear, but the general progress still escalates from the more grounded characters dealing with more grounded issues from before the titular tournament, to the more plot-heavy characters going through more significant events, so that things later progress to the tournament and you can get a clear sense of whom officially beat whom (you generally play as the winners through their victorious fights), after which the characters and events you play through focus more squarely on the ninja characters and their conflict with their high-tech antagonist that breaks out after the actual tournament is done.
Also, props for Tekken 7 for sneaking in flashback of significant series events during its story mode scene when someone gets knocked down, it illustrates the history and stakes of it all during the actual gameplay,which was a neat touch.