I personally think it's crazy talk claiming fighting games are easier to get into than shooters (I'm not gonna comment on MOBAs as I don't play them).
I think one huge difference is having a general idea of how to improve. If you get destroyed in a shooter, then you usually have some kind of idea why it happened. The other guy might have spotted you faster. He might have had better aim. He might have flanked you. Most shooters also have killcams, which makes it even more apparent how you lost.
Now, look at fighting games from a newbie's perspective. They could be facing someone who's simply spamming the same safe or gimmicky move, getting destroyed by it, and not understanding why. Fighting games are awful at explaining their own mechanics, and worse than that, they usually focus on teaching the wrong things.
The most important thing in a fighting game is knowing what to do in neutral. But fighting games usually do one of the following: not explain it at all, only explain it through a big wall of text (I don't mind that personally, but I think most people ignore these kinds of tutorials), or the most common thing: show the player a long list of combos. Knowing how to execute combos won't be of much help if that player doesn't know how to actually make the first hit of a combo connect.
I'd say it's practically mandatory to have a friend teach you how to play fighting games. That, or you need to find a really good tutorial online.