My two cents and personal opinion: from a sensory standpoint, anything you do in the mash, from changing saccharification temperatures to complicated step mashes to decoctions, has a relatively minor impact on your beer. I’m not saying zero impact, and there can be fairly dramatic changes in things like efficiency and attenuation. But in terms of the sensory properties of the beer, the effects are small. Small, as in, Brulosophy can’t reject the null hypothesis. (Whatever you might think of Brulosophy, it’s hard to argue that an effect is OMG HUGE when most average drinkers can’t tell the difference side-by-side.)
Recipe changes, on the other hand, can make a major difference — that flaked barley will absolutely change the mouthfeel in a way that will be obvious.
To me, it just makes sense for a beginning brewer (and many expert ones) to keep the process simple while they’re figuring out what their ingredients do. I suspect that for the OP, this translates to “no, the protein rest isn’t necessary at all, but the flaked barley really is.”