Rommel and Hitler actually got along very well. They had a bit of a symbiotic relationship going on, given that Rommel saw on Hitler an able politician that could do what was needed to be done, while Hitler saw on Rommel an able general and a self-made man, rather than someone that was just there due to birthplace. Rommel was also perfectly happy with taking advantage of this relationship (as was the case of the appointment of the 7th Panzer to him). Rommel wasn't in support of the plot (at the time, he was knocked out cold because his ride had been strafed and he got wounded as a result), and in fact, when he came to learn of it, his first reaction something among the lines of "I can't fathom that anyone would want to kill the [email protected]
While his reputation is overblown, to say that he's just "above average" is a bit of a disservice. And he certainly possessed, if not at least developed, a strategic grasp. This can be seen when he argued with Kesselring over the handling of the German forces in Italy, where Rommel favored a more defensive approach on northern Italy, as he foresaw a rapid collapse of the front lines otherwise (owing the materiel disparity between both sides), Kesselring favored to hold the line far, far south, with optimism that'd be more appropriate following the string of successes in 1940, rather than the chain of defeats of '42 and '43. While Kesselring was ultimately right, it was in part due to reasons that he could've certainly not foreseen (such as Clark opting to go capture Rome, rather than trap and wipe out the 10th Army following the breakthrough on Monte Cassino). Furthermore, Rommel's grasp of the disparity at a strategic level (in contrast with how other German Generals and Field Marshals saw it) also manifested on how he wished to conduct the defense on the event of the landings, with him favoring concentrating the forces closer to the frontlines in order to defeat any attempts of establishing a beach head (and minimizing the possibility of the Allies leveraging their advantages), while the general stance was to have them set in reserves in the rear lines, and then be mobilized in counter attacks. Which of course, was a problem when these were intercepted and harassed by Allied aircraft (one of the many things that Rommel had accounted for when trying to put his defensive plan in motion).
Granted, stuff such as going off to celebrate your wife's birthday on the day the landings took place (in a timeframe where aggression was to be expected) is simply too much of a foolish mistake to make for someone of his position. Then again, his superiors didn't act in a much less inept way, and the complete lack of intelligence and reconnaissance on the German part only made things much, much harder. So, while Rommel was far from a strategic mastermind (even if he wanted to believe he was one as), he was far from having virtually zero grasp on that aspect.
While luck's certainly been at play, recognizing openings and opportunities to strike are, in fact, capacities that a shrewd commander has. You don't make it through the near-entirety of World War 1 (accounting for the times he wasn't on the front lines due to injury or refit), and much of World War 2 by just being a luck sack, especially considering how much of a daredevil he was. Less capable men would've either perished or been sacked far, far earlier than when Rommel took the pill.