I can't really say for sure how much the handle thickness has to do with it, but I have one that I have had since It was new. It was one of the first HD editions, but I have since lost the decals and refinished It. I dropped the weight bolt out of It, and found Myself going back to the cue a lot as well. I'm pretty much just thrown into tuff matches once a week sometimes less when I can't show up to play, and get very little practice anymore, so have to perform on demand, and I still switch back and forth occasionally between the one I built and that cue, one night I hit better with one cue, and on another night I hit better with the other one. I started out building 5/16 pin cues, but now build most of My cues with a 3/8 pin due in part to the fact that the cue has performed so well for me over the years.
I am seeing the same trend that Dick mentioned. Ironically I just built a shaft last week for a guy that has two old Mcdermotts, and He wanted a 30" 14mm shaft for one of them. I talked him down to 13.80mm to make tipping the shaft a bit easier. I stuck It on My handle and hit some balls with it and really liked It. It had a harder ferrule, and hard tip, but had the control of a softer setup. Solid hit too, actually the first words out of his mouth was that It was solid feeling, and can I build him one for his other cue. That shaft did not have a high grain count, I forget what it was, but I'm sure It was under 12-13 gpi. I hand tapered the shaft to final size, and as I mentioned really like It, and want one for My cues, so I told him I may need to borrow the shaft sometime to make a taper bar for future use. I have 2 other orders to fill from other people that have been after me for a while to build the same diameter. I still have people that want something closer to the low end of 13mm, but many people want to go larger.
The handle I built and use, is not quite as large, but It is a straight taper, and not much smaller feeling then My Mcdermott. I have about 4 shafts that can be used on either cue. It's the only other cue I use that was not built by me, although all of the shafts were built by me, as the original shaft warped many years ago. No doubt probably due to the fact I only used It to break with for many years when My players were steel jointed 5/16. Now My break cue and jump cue are of My own creations. Pretty happy with the purple heart shaft on My break cue. Same size pin, really stiff shaft.