The problem is you did not mention what you get use out of. For some people the Disney card can be useful, not so much for the actual rewards, but if you're a real Disney fan, you do get nice discounts at the Store and online, occasional special deals, etc. So worth keeping alive just for that if you're a big fan. The rewards are not very exciting but the fringe benefits are nice. My grandmother has had one a long time and she likes the extra benefits.
Now, looking at your list, I think the PNC Cash Builder can go as your QS gives you 1.5%. The Slate is useless beyond a BT and is only a $600 limit, so I'd move the limit and/or close it out. I think having Double Cash on top of QS can be redundant, so depending which one you like more, you could pare down one or the other. (I have both at the moment but am keeping both because of the lower limit on DC).
You also have a QS1 that you could close. There's no point in paying for it when you have a plain QS. There's also no point wasting time to get your fee removed since you already have the better card. Unless you plan to use the Apple financing again, it's a waste IMO. Total one time use card.
Discover and Freedom are very very similar throughout the year. Opinions vary but you probably don't need both unless you are heavily transferring your Freedom points to CSP. On a pure cash back basis I find Discover more broadly useful with less tightly defined categories during the year (home improvement vs just Lowe's on Freedom etc). However if you really prefer Freedom then you may not need the Discover. Also, do you spend enough and travel enough to really justify the CSP long term? If not, that's a case for preferring Discover.
Finally, your Amex ED is not very useful at $700. Either try to get a CLI if it's old enough or just close it. It's doing nothing for you.
So to sum it up -- QS1, Slate, Cash Builder, Apple and Freedom/Discover are definitely candidates for closure IMO. By my quick count you have 20+ cards and I definitely agree it's too many. I'd also evaluate your store cards like American Eagle and JCP etc and really decide if you use them enough to warrant them.
