> As a manager, I actually find people doing "big picture" thinking quite annoying to deal with

That's a bold statement. You've made your job easier, at the cost of creating a culture of "not my job". You assume you can handle all the big picture yourself. That way lies micromanagement.

Maybe your team requires that right now. Only you know. But you should also ask yourself why you sound like your team is annoying you. In the quote above, in "to hear them tell it", "some people just can't handle it".