So I'm not saying strategic vs tactical is a binary; it's a spectrum. And where to fall on it is hard; I think we're in agreement here.
But, you mention you've been overridden by bad executive fiat on occasion, and also made forays where you shouldn't have because you didn't have the bigger picture. The 'right' course of action to address both of those as your manager would be to make sure you understand the bigger picture, and then to let you (or whoever bears the effect of the decision) make the decision, not to make it for you, nor to let you stumble blindly into a bad one.
In terms of Jobs, Musk, Ford, Bezos, strategy informs tactics, and tactics inform strategy; as you say, you have to ask questions and seek to understand; you also need to communicate and help people connect the dots. But that's different than daily status reports and directives. Seeking to understand the why, rather than endlessly try and stay up to date of the what, is the goal. If you've built a healthy org, they'll raise up concerns about the what when they need to; even when they do, the fix for a bad situation is never focusing on the situation ("still in the hole?" "yep"), it's helping navigate a way out of it ("quit digging; here's a ladder, our new goal is climbing out"), and then figure out how to avoid it in the future ("how did we get in that hole? Why did we keep digging ourselves deeper? WHERE DID ALL THESE SHOVELS COME FROM?!").
And, yes, strategy is often boring and predictable; given the same knowledge, the same set of inputs, most people would make the same decision. It's one reason why I don't think executive pay is justified; I'm not intending to mythologize it or something. Just point out that as you climb a management hierarchy, your concerns move along the strategy/tactical axis toward the strategy side, and that oftentimes bad, poorly informed decisions are due to execs moving too far toward the tactical.