One thing I've found that I think makes it so enjoyable for me, is the mix of tactics/strategy with the "shoot 'em up" aspects of actually carrying out an attack.
A game that consists of nothing but moving along a mostly predetermined course and trying to destroy the next hostile element that appears is fun for a while, but only for so long.
OTOH, when it comes to the strategic element, I don't want to command an entire army/navy, build an empire, or anything as grand as that. That's too much like
work.
SH3 seems to give me the best of both worlds. I get the thrill of encountering and doing battle with an enemy, and I have a lot of discretion when it comes to how I pursue my own personal "campaign" once I'm out at sea. But I'm not bogged down in trying to oversee the entire Battle of the Atlantic, much less "my side" in the conflict as a whole, and compared to a lot of "shooter" games the variations in terms of when and where I'll meet the enemy, who he'll be and how much of a threat he'll pose, seem almost endless.
Plus I love the fact that, unless I want to be, I'm not tied to the computer, my hands wrapped permanently around a controller or poised over the keyboard/mouse, for the duration of a playing session. I can load up the game, pick up my career where I last left off, and once I'm out at sea with a course set and every station manned to my satisfaction, I can relax and read a book or get up and do some chores and come back to the game periodically to check on our progress or respond to a shout out from one of my crew. I don't have to be right there looking over their shoulders every minute, but I do have to remain mindful of our general situation and the fact that I may need to jump into action at any moment. And that, I think, adds to the immersion factor for me.