He wasn't protecting Brown or Care by dropping them - he was trying to ensure he had a second option.
Since Goode was dropped, no-one else had played fullback for any length of time. Jones was starting Daly repeatedly - despite his weaknesses - to give him time to adapt to the role. Brown isn't a good bench option, and since he wasn't going to start there's not much point having him in the XXIII, but he was around the training squad presumably to help Daly.
Likewise, Eddie had only really had Youngs, Wigglesworth and Care in the squad throughout his tenure and didn't have a back up option with any international experience. Since he insisted on only having 2 scrum halves in camp, dropping Care allowed him to look at the alternatives, even though he didn't give them much game time.
But in the RWC, you need at least two players who have been proven to be able to play each position, and ideally three given England's tough schedule. At fullback, neither Nowell nor Watson have played the position internationally, though Watson showed some promise in the Lions warm-up games. Unless he wants to recall Goode (which would delight Stuart Barnes but worry everybody else), his only experienced options are Brown and Daly.
At scrum half, Youngs will only just be coming back from injury, Robson and Spencer have almost zero experience at that level. Wigglesworth and Care are likely to make the training squad at the very least.
Eddie is idiosyncratic, but he's also been to multiple RWCs and coached one winning team, one finalist and a Japan team that outperformed all expectations. He has his flaws but he knows how to manage an RWC tournament, and betting on having one experienced option in a specialist position is not part of doing that.