I think the hierarchy bit goes back to Meghan's fundamental misunderstanding of her position and its obligations. I'm not saying class privilege has been eliminated in the US - far from it! - but for the most part, people in higher-ranking managerial positions are there because they did something to earn it. That's usually some combination of relevant skills, qualifications, and experience, and it usually involves convincing HR or some other higher-up that they're the best choice out of all the other applicants. That doesn't necessarily mean they really were the best choice, and it certainly doesn't mean that they should be horrible to their staff, but it does mean that if a subordinate wants to give them advice about some aspect of their job, they shouldn't necessarily defer to the subordinate's judgment over their own. The same was true for Meghan in previous jobs. She got her acting roles because (presumably) she did well enough at the audition to convince those in charge that she was the best person for it. She's not going to let the coffee-fetcher tell her how to be a better actress, because what does the coffee-fetcher know about acting? Maybe that's not the best attitude to have, but it's understandable and very common in that situation.
The problem is that she failed to recognize that being a working royal was different. She got that job for one reason, and one reason only: she married a prince. If Harry hadn't wanted to marry her, she might have been the best Duchess the world has ever seen, and it wouldn't have mattered. If she'd been terrible at it, he'd probably have married her anyway, and she'd still have gotten the job. But she seemed to view that fact that she was a Duchess as proof that she knew more about the job than her staff ever could. That's not really a workable mindset for jobs one gets due to family ties rather than any kind of merit-based process, especially when it's someone new to the role ignoring the advice of support staff who've been doing this exact thing for decades.
I think this is part of where the concept of "noblesse oblige" comes from. A fair-minded person who knows that they're where they are entirely due to an accident of birth isn't going to feel like their inherited position gives them any fundamental superiority over their staff members. Positional and supervisory authority, yes, but not superiority of knowledge, skills, or judgment. Approaching that type of position with the mindset that you know better than the staff because they work for you rather than vice versa is a recipe for disaster, because you're probably wrong. The rest of the royals know that, perhaps because they were raised with it being normal. But either no one tried to explain it to Meghan, or she just didn't want to hear it.