I used to be very wary of solitaire wargames. Not, mind you, of playing two-player wargames solitaire, but of honest-to-gosh solitaire designs. Partially, my reticence was somewhat aspirational: I might be playing both sides in this WW2 game, but the possibility existed that someday, someone who would dig the game would be sitting on the other side of the table. Whereas if I plunked down some of my hard-earned cash for a solo-only title, that possibility - however rarified and improbable - no longer existed. And, when you're on the sort of budget where you can only buy maybe five or six games a year (that's games, period, Euros and wargames both), buying a $60 solo game about submarines doesn't seem like a sound investment.
But more than that, I was leery of what I had heard about solitaire wargames from reading various forums and watching video reviews. From the outside, the decision-making didn't seem as rich as in a two-player game (even a two-player game played solo). Some of the games more-or-less "played themselves", with you just being along for the ride, a captive if willing audience. That might provide an exceptional narrative experience - there are lots of folks who swear by those kinds of games - but it doesn't look all that appealing to me, or at the very least, it's not what I want out of a game.
There was another, very popular class of solitaire games that often had you do little else but rolling the dice to try to slow down the advance of this enemy column or that one, said advances being dictated by card draws. You win such a game by rolling better dice and shuffling the cards in the right order. Such games are essentially "stateless". The game has no memory, and your past actions have no impact on what happens next. Some games solve this problem by adding more bells and whistles, more things that the player can control and which can make the player's position stronger or weaker. Those feel more like a "real" wargame to me, and I get a lot more out of 'em.
One of the things I tried to do with my Agricola, Master of Britain (as well as its follow-up, the forthcoming Charlemagne, Master of Europe) is to have the behavior of enemy units influenced by your actions. The short version is that there are three cups containing enemy chits, each reflecting an attitude toward your rule ranging from Friendly to Unfriendly to Hostile, and that every action you take blindly moves chits from one cup to another. Military actions such as Suppression and Battle tend to push the enemy toward a Hostile stance, while softer actions make them more peaceable. You don't know exactly who is in which cup, but by building settlements (in Agricola) and churches (in Charlemagne) and keeping a presence within a region, you can determine which cup eliminated units go into. If you go hard military, you'll have few allies and lots of hostiles that could spring up any and everywhere; if you go in the opposite direction, there's less adversity to your rule (and, with less opportunities for glory, less chances to score VP). The mid-game is formed by the early game, and the end-game by the mid-game; feedback loops are created which multiply your actions over the course of the game. People who are very good at these games know that the real secret is how you influence the cups less than what's going on over on the board itself.
I'm working with a first-time designer on a very promising solitaire game that tackles this problem from another angle. During each game turn, each enemy unit draws X number of chits, needing Y number of successes to advance to the next space. Y is equal to the defensive value of the space, which you can bolster, and X is equal to the strength of the enemy unit, which fluctuates from turn-to-turn, growing as it receives reinforcements (which you can try to stall) and shrinking as it suffers losses (which you inflict). So you don't get that weird kind of situation where you hammer back a northern army six turns in a row, only to have the next six card draws bring them right back to your doorstep. You can directly frustrate the enemy's ability to advance over the long term. Your choices matter.
You don't necessarily need to be able to influence the enemy's ability to act in order to feel like your decisions matter, however. The big problem with many of the "draw a card to see where the enemy advances" games is that you have a static deck that you shuffle at the beginning and run through once, with each card getting played in turned. You can however impart a sense of memory to the game deck without being able to influence it. Consider for example Matt Leacock's cooperative game Pandemic. This is also a game that solitaires very well, even when you have four other players at the table and guys, we would have this all under control if you all took your turns exactly as I tell you how to do it. It uses a random card draw to determine where the nasty disease cubes will pop up next. The clever bit is that when an epidemic is called for, all the discards are shuffled and put back on top of the deck. All those cities you just cleared out are about to relapse. Throughout any given game, the same cities will get hit again and again, with the same cities getting threatened. You know where to concentrate your efforts, and you can figure out what you need to do to neutralize the threat posed by a given area, and, oh, crud, there it goes again. Something like that could work very well in a solitaire wargame, creating a sense of narrative and purposefulness that you don't and can't get by running through the deck, one card after another.