I've discussed this with Dudley before as I'm sure most know that's what he says too, but I disagree.
I'm curious to the "how" this would be the case on your findings. If a bow is shooting a bareshaft, and let's say you put it in a hooter shooter, and its pounding the same hole time after time, what is causing it to suddenly shoot poor groups when you put fletching on it the shaft?
This is easy to replicate in a non bow way to see. Take a broom and set it down on the ground handle end down. Then let go. Which way does it fall? Who knows. It'll be different each time.
Now, stand this broom up the same way but with a very slight lean to the left. Let go. It falls left. Every time.
The same is said with arrows. You don't want an arrow to knuckleball out of the bow. Perfectly straight bareshaft scenario.
If your grip pressure isn't 100% perfect every time, the arrow starts in a new direction out of the bow. Like the first example with the broom. If your facial pressure changes, the arrow starts in a different direction. If your release hand comes back more or less to the left, right, up, or down; the arrow comes out differently each time.
Sure you may have, "Perfect bareshaft flight" but what did that do for your groups?
Take that same arrow and give it a slight direction. Then the arrow starts out of the bow the same way each time. The second broom scenario. This allows you to have a more predictable group placement on the target. Meaning not sporadically spread out all over the target. Closer together in one direction.
Why would this be important? Well, it helps you adjust your sight to play the averages. Just like an archer sights in for a high x indoors if they have a tendency to shoot the occasional weak shot and hit low. This is playing the averages.
That's why group tuning is so important. You can put small adjustments into the arrow rest and see your results in your groupings down range. You can continue your adjustments until your groups are as small and consistent as you're capable of making them.
You shoot arrows for score with fletchings. Not as a bareshaft. Tune for how you score just like you practice for the type of game you'll play.
Practice doesn't make perfect, perfect practice makes perfect.
I challenge everyone that insists on perfect bareshaft flight to group tune and adjust the arrow rest to see what you get. Every archer I've ever done this with finds better groupings by adding a slight direction to the arrow.
Start with dropping the height of the arrow rest down in a small amount. Then after you find the vertical spot that works the best, start adjusting the arrow rest out away from the riser and see if it's better or worse. Worse? Adjust it in towards the riser.
I've found my left and rights stay a lot closer to dead center than my ups and downs on my arrow rest adjustments.