Franchise mode is the closest thing to the real world of being a GM and a player. I always said to myself "man if I were in charge of my favorite team I'd make these moves or those moves." Franchise mode allows me to do that, and control nearly every facet (or at least what the developers provide) of a franchise and then play out those decisions on the field. Diamond Dynasty as some have mentioned is more like fantasy baseball, which isn't my cup of tea. Don't get me wrong you can still have the fantasy baseball aspect within franchise mode given there is a fantasy draft and if you manipulate the game in such a way can get results of a fantasy style of play. I know you said to stay away from the multiplayer thing, but given the fact that the way I play franchise is 100% not the way EVERYONE plays franchise is definitely why I stay away from DD. Multiplayer online also tends to be a toxic environment, so there's that too, which is why I was devastated when they removed online franchise b/c that was how you could play actual Franchise mode in a private league with friends who played with similar philosophies making it non-toxic and super fun.
But if you're talking about how to get more enjoyment out of franchise mode as it is now, I would suggest trying to keep your play in line with how a real life club would operate. For me I try to stay within the realm of realistic decisions and keep things on the hardest difficulty to mimic how hard it is to actually run a club. Just for example, when it comes to the amateur draft I could easily create a save point prior to the draft and see what players end up with high potentials and overalls and then go back and reload that save point and draft those players to totally load up my team. But I totally stay away from that type of play because I want to be rewarded for sticking to my guns and living with the decisions I make and getting better at the game. As another example my team right now is ranked, I think, 3rd or 4th in terms of the 5 overall ranking categories: Pitching, Speed, Defense, Power, and Contact. My power rating is 25 or 26 and it shows as my team has a very low number of homeruns. So I have to play to my strengths in order to be successful. I could easily manipulate the game and inflate my budget and trade and acquire a ton of power hitters but I know that's not in the realm of realism.
Sorry for the long post, but I wanted to give you a solid in depth answer. Hope it helps, and hope you get more enjoyment out of franchise mode.
Cheers!