Take a minute and reflect on the fact that you're arguing Turing had nothing to do with mathematical logic.

His doctoral advisor was Church, his work based on Gödel, his thesis named Systems of Logic Based on Ordinals.

Comments like these show the perils of treating mathematics like a cookbook. It's a very limiting mindset.

I'm arguing that Turing's impact on computing (most importantly, defining the Turing machine) didn't have much to do with logic. His work on logic is also important, but I don't think it's useful for a programmer.

On the other hand the fact that you're reaching all the way to Turing to exhibit a clear impact on practice suggests that for the programmer without such grand aspirations there isn't much to be gained.