You can cancel anything you want, there is no "should" or "shouldn't". Keep cards the way you feel comfortable.
If you no longer want to use a card (let's say Cap1 QS after getting Citi Double Cash), you may cancel it or sockdrawer it (or still use it). Except for available credit, closing the card has no impact on your credit score, so it's not necessarily a bad thing. If you just don't use it, then you still have to monitor that account for fraud.
Practically speaking, after getting the Double Cash your BoA cash will only be used in gas, BCE only be used in grocery, for which both have caps, so you might still use these two with fewer swipes.
Your Blue just gets sockdrawered already, you might close it. Or, see if there is a chance for product change to Everyday if you wish. This is for Membership Rewards rather than cash, giving you flexibility to use the points elsewhere. You probably cannot change Blue to Everyday
, despite Blue earns MR points.
For Cap1 Quicksilver, you might eventually want to close the card.