I've decided to go for more of a compromise rather than flat out selling my whole collection and substituting it for an Everdrive. I've been selling off games for the NES, SNES, and Genesis that I either did not play or own growing up because I have no attachment to these games since they are not systems I'm super into and while I like many of the games, I do not need to own the single carts of them to enjoy them. My attachment to games I actually played during my childhood goes beyond being able to play them however; I like looking at the cartridge, the manuals and box art like I did when I was a kid, bringing back memories of owning these games back in the day.
So my advice is to sell games you do not have this nostalgic attachment to and keep the ones you do. You'll be a lot less likely to regret selling some of your collection if you do it this way.