I think if a photographer uses just a couple of films any form of agitation or rotary processing can work because you learn the quirks of the film and developer, put bluntly you learn from your mistakes. But if a photographer uses a wider range of films and likes to change developers I think it's worth sticking with the twiddle stick because it eliminates common faults or accidents of inversion such as surge, foaming, air bubbles, etc. None of these things come into the equation with the twiddle stick because not matter what developer or strength of developer you will not get surge around the sprocket holes, it can't foam, or make air bubbles etc. A different approach from 'I've never had a problem (yet)' to 'let's not start out by encouraging potential problems'.
So I use the twiddle stick almost exclusively with Paterson tanks with the exception of a couple of film and developer combinations where I just swish the developer gently in a circular motion. But the twiddle stick shouldn't be used like a ham fisted gorilla, gentle turns are all that is required, you aren't trying to create vortices, just enough to keep putting fresh developer on the film. I think the twiddle stick is also more reassuring for techniques such as semi-stand developing where you don't have to worry for three or four minutes if you banged the tank hard enough to disperse air bubbles after the previous inversion. The whole point of using the twiddle stick is to mimic the only sure fire way to process successfully every time, which is a deep tank, where you aren't plunging the film in and out of the developer by way of agitation, just moving the spiral around in the liquid, usually D-76 the last time I used a deep tank.