Loads of counterexamples:
R U R' F' L' U' L F
R U2 R' U2 R' F R F' (of course you could argue that this is just Antisune cancel into sexysledge…)
R U R2 F R F2 U F
R U2 R2 U' R2 U' R2 U2 R
(the last two could be contorted into commutators if you allow nonstandard moves like mirroring the cube state)
(edit: The first two
are commutators, but not of the typical insert/interchange kind; see post #11 by Christopher.)
You should also be mindful as to how much you're willing to allow combining commutators, because
any move sequence where the turns "balance out" can be rewritten as a sequence of commutators. Just to take a silly example, R U R' U' R' F R F' already is a concatenation of two commutators: (R U R' U') is a commutator and so is (R' F R F').
(Related reading:
commutator subgroups.)
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The actual feature you're noticing is probably more closely related to slicey shenanigans.
R U R' U'
R' F R F'
r U R' U'
r' F R F' = R
M' U R' U'
M R' F R F'
These two things differ only by two slice moves and so the second alg can be viewed as inserting M' U R' U M U R U' (which is a commutator that does an edge 3-cycle) into sexysledge.
This logic applies to
any algs that are slice variations of each other. For another example, consider Sune vs wide Sune:
R U R' U R U2 R'
r U R' U R U2 r' = R M' U R' U R U2 M R'
This one is equivalent to inserting [M', U R' U R U2], which looks funny, but turns out to be just an edge 3-cycle. And indeed Sune and wide Sune differ in their effects by an edge 3-cycle.
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Yet another perspective you can take is that you're really looking at different ways of taking out pairs/blocks and seeing how to combine them; the "difference" between two ways then gives you an alg that preserves everything you want to preserve (and possibly affecting things you don't want to preserve).
Look at just R U R' U' R' and r U R' U' r'; these affect the F2L pieces in exactly the same way, so in a sense they're "interchangeable". With any last layer alg that starts with one of those, you could modify it to start with the other and it'll still be a last layer alg.
Example: widened T perm r U R' U' r' F R2 U' R' U' R U R' F'.
Something else you can do here is to try R U R' U' R' R U R U' R' (which does nothing), then modify the first half to get r U R U' r' R U R U' R', which is now a last layer alg that
does something. This is also equivalent to r U R' U' r' (R U R' U' R')'.
Or look at R U R' U versus R U2 R'. Start with Bruno:
R U2 R2 U' R2 U' R2 U2 R = R U2 R' R' U' R2 U' R' R' U2 R
Modify the initial R U2 R' into R U R' U:
R U R' U R' U' R2 U' R' R' U2 R
Modify the final R' U2 R into U R' U R:
R U R' U R' U' R2 U' R' U R' U R
Now you've created a U perm!
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Something else to note is that r U R' U' r' F R F' is a corner commutator,
but not when written like this. If you rewrite it without wide moves, the commutator structure becomes extremely apparent: L F R' F' L' F R F' = [L, F R' F'].
Same for R U R' U' R' F R F', which is a block commutator, but again, not when written like this. Rewrite it
with wide moves to get: l F R' F' l' F R F' = [l, F R' F'].
