What Pat said it's to stiffen the upper bout and belay, hopefully the eventual folding of the neck into the body necessitating a neck reset.

When you look at a guitar head on from the front and it needs a neck reset I can usually see it because the lines of the bindings where the body meets the neck turn inward as the neck is folding into the body. You can see the body deformation if you look carefully.

These "paddles" couple the block, sides, top and for some makers the upper transverse brace into one assembly pushing back on the tendency of string tension and time folding the neck into the body.

I worked on a Martin D-28 Modern Deluxe last week that has a paddle and that new 4 mm truss rod I posted about here on the OLF. So even Martin is using paddles on some models these days.

Is it a good idea? Not sure. I don't see any harm beyond any possible sparkle and tone in the UTB (upper transverse brace) region being dampened by the additional stiffness. Many would argue that there is no tone to be had or preserved in this region. They may be right.

My guess since we need time to know is that it's probably a good idea.

I'll add since this is pictured on a cut-a-way. Did you folks know that with the advent of the cut-a-way it's possible that we are seeing the need for neck resets sooner? I don't have the data but I have seen on my bench cut-a-way guitars that it's neck reset time and unusually the neck is now not just folding into the body it's sideways angle has changed... as the cut-a-way side has collapsed far more than the non-cut-a-way side. I had one on my bench from a major maker like this that was only 3 years old.... and it needed a neck reset.

This is rare, no need to worry about cut-a-ways but if I were building again I would likely be keen to use a paddle on a cut-a-way just in case anticipating that the asymmetrical structure may not resist folding as uniformly as a symmetrical structure.

If you use a paddle be sure to do dry runs with truss rod access to be sure it's accessible and be sure to put a hole in your UTB. You would be surprised at how often that hole is forgotten....

If the extension goes out past the fingerboard edges on either side it might help to prevent shrinkage of the ebony from pulling cracks in the top on either side. That's what the 'popsicle stick' brace is supposed to do, but doesn't do very well. I make my extension just a little wider than the fingerboard at the sound hole end, and wider at the base of the neck, so the edge doesn't run along a single grain line and concentrate the stress. I've done this for 25 years or so, and it seems to be working so far.

I've also been using 'A' braces, about 1/4" square or a bit more, on either side of the sound hole. The upper ends of these plug into the neck extension. The UTB is notched so they can run through it, and the lower ends plug into the upper arms of the 'X' brace on steel strings, and the the waist bar on classicals. I use a patch of (usually) spruce around the hole to approximately double the thickness of the top there, with the grain running slightly across the top grain; about 3-5 degrees, to help avoid cracks there. The 'A' braces taper to the height of the doubler at the lower end where they are inlet into the brace. All the bracing around the doubler fits tight. All of this is meant to keep the neck from shifting in in case of accidents. I've had two with this set of features that I can remember that have been knocked over or pushed off a table so that they hit on the back of the head or on the neck. Both had large dings in the neck/head, but no further damage. I'm sure, from prior experience, that they would have pushed in otherwise. I hate having to fix stuff I've made...