I guess I'm just the opposite: I'd rather move the clutter from the tracks area down into the bus pane, which I keep hidden during much of the mixing process. That's why I'm reading this thread, in hopes of gleaning some compelling reason to use aux tracks or patch points.
The best justification I've identified so far: combining multi-instrument ensembles such as drum kits and orchestral string sections into an aux track. Kick, snare, overheads, etc. become one instrument, "drums". Violins, Violas and Celli become "strings". A bus can do that, of course, but what the aux track does for you is position the combined meta-instrument up in the track pane where it belongs during mixing, rather than down in the bus pane far from the action.
You can also use aux tracks and patch points as a way to bounce a reverb return or to freeze other high-CPU or high-latency effects. That would have been a great help two CPUs ago but nowadays it's more trouble than it's worth.