Disclaimer, I've never bothered with a protein rest, but have thought about including one on some of my wheat-heavy brews, so thought I would throw my theory out and see if it makes sense to anyone else.
Since I can't help but try to figure out the science behind things, I was trying to remember what the actual enzymes were that the protein rest is meant to activate, so I went back to John Palmer to see what he said
(apologies if this has been updated in the newer versions, I don't have mine in front of me).
If he's correct, there are actually two groups of enzymes active at typical protein rest temps. The first concern the proteases that will help to break down proteins in under-modified malt. These proteins weren't fully broken down during malting, so cutting them into smaller pieces will facilitate the release of starch from the grain. This will also help to cut down on soluble proteins in the wort, which can help if you get chill haze, but if you go too far you can start to diminish the body of the beer.
The second set of enzymes are the beta-glucanases that ASantiago mentioned that will break up the larger starches present in wheat and oats into smaller pieces so that you can avoid problems like stuck sparges. This would also presumably release easier substrates for the amylase enzymes. He even mentions the possibility of aiming on the lower end of the "protein rest" (~100-110F) if you want to avoid the protease activity.
So here's my thought, check and see if it makes any sense.
1. If I was using flaked/raw/rolled wheat or oats (since not malted, would fall under the under-modified category) a typical protein rest around 120-130 would be a good call, both to break down some of the proteins and to break down some of the gummy starches.
2. If I was using malted wheat or oats (not sure about rye?) I could assume that so long as it wasn't under-modified a protein rest probably isn't necessary. However, a short protein rest, or even a short rest below protein temps (100-110) might help to break down some of the starches, especially if I was having stuck sparge problems.
3. If I wasn't using any or very little wheat or oats, the protein rest might not give any appreciable benefit unless I was also having trouble with another factor, like chill haze.
Sorry for the long post, but does any of that makes sense?