I do know a fair bit about the media & PR industries and now own my own small business in a related industry - just to establish my bona fides without being too outing.
I can confidently say based on my 3 decades of professional experience: they do not have good PR counsel, or if they do, they're not taking the advice.
What I suspect happens is that they pay for initial strategic ideas (activism around social media / faux royal tours) but then, either due to arrogance or due to lack of funds, they don't pay the agency to develop the idea or implement it tactically. They try to do that themselves with probably a handful of directly employed staff. That's why everything is poorly done and looks amateur.
They don't appear to employ a speech writer either - Harry's speech and panel discussion with the Diana Award winners regarding social media was so poorly done I was watching through my fingers at some points. He was stuttering, spoke brokenly and his wors had no underlying substance. He may have been unwell/having an off day but he clearly hadn't role played that appearance with a proper adviser and he hadn't used a speech writer either.
I also suspect that Meghan does media relations herself. I think it's literally her placing stories with Us Weekly. She only seems to have contacts at that one publication and she didn't seem able to get ex-employees to praise her naturally and convincingly. Her approach to media is OK for a hustling d-list actress but not for a globally respected activist which is what she positions herself as. The people who play that role well, the Obamas or the Clooneys, they have dozens of really experienced experts in media relations alone.
So in summary, I think the air of amateurishness and half-assed-ness that surrounds their public endeavours is simply due to arrogance or lack of funds - they're either not paying for best-in-class agency advice or they're paying for the advice and not taking it, or not going on to pay for the implementation.
I know that Sunshine Sachs fired them for non-payment of bills, that's well known.
As for the attacks of their personalities, that is an inevitable result of explicitly setting yourself up as morally superior to another group (the RF in this case). If your product is your personality, then you can't complain when people test-drive the product, find it lacking, and decide to say so publicly.