I got hung up on the claim "Touch is by default idempotent. ... A second call won’t have any effects". The whole point of touch is to have an effect every single time you run it. It updates the file atime and mtime. That may seem harmless in your application, but it's definitely not no effect. Also promiscuous touching is the source of a bunch of bogus last modified dates in source code bundles.
I've heard Idempotency confused with Consistency. Idempotency is where a function f can be applied (as a composition) multiple times and it gives the same result, so Idempotency: f(f(x)) = f(x) . Whereas Consistency: f(x) = f(x) = f(x) . An example of an idempotent function f is RaiseToThePowerZero(x) on x > 0. We usually take consistency for granted, so it's perhaps better to think of an example of a non-consistent…
Sorry, what does idempotency have to do with convolution?