Can those amongst you have have opted for a crooked reg bar rather than the straight bar design on your full sets share your reasons for choosing the former over the traditional “look”? Cheers.
I have had both. I seem to be some kinda of freak in that I could never play a straight reg’d set without feeling pinned to one side of the set and unable to pivot to reach the lowest reg keys. A wrap-around settled all that. It also puts the pipes practically flat in my lap, which also facilitates greater access to the keys.
Fixed straight bars require disassembly to fit into a reasonably-sized case.
What tom said.
As the bass bar sits in the crook of your left arm, the range of possible angles for the stock/drones/regs is limited.
As I also like the whole shebang very low, if I had the straight bar I’d have to adopt an even more simian posture to play.
What is non-traditional about the folded bass reg. bar? It has been in use for well over a hundred years. Conversely, some prefer the straight bass bar. Whatever works!
I think players with the ‘straight’ or ‘long’ bass bar tend play at a higher position. You will often see players with the mainstocks set high on the bag and supported by a cord or strap for stability. If you prefer a lower position with a long bar more nearly flat across your legs, then you would, as bensdad points out, have to hunch way over to get full access to the regs. 'Course everyone is built a little differently, and YMMV.
Bob
Other than one Willie Rowsome set (owned by Glands), are there any old Irish-made sets with a wrap-around bass reg bar?
O’Mealy was one Irish maker who certainly used the Taylor-style ‘U-bend’ regulator style on many of his sets.
My old Taylor-style set has the wrap around bass reg, and I would agree with others as to the advantages. It certainly (for me anyway) makes the regs more comfortable and more accessible laying across the lap. So I certainly like the design for a concert pitch set. Whether it would feel ‘right’ for a flat set with a longer stretch to reach the regs, I don’t know.
I am upgrading to a full set from a 3/4 and have decided to go for the Taylor style bass regulator.
I know only a few makers offer this style. Also the price seems to be more for this too. That could be why you do not see many sets with this bass reg. Also many might not even know about it.
I will get mine in about one year. 
Some pipers prefer the support and control offered by the straight reg bar.
I wonder if Johnny Doran ever played a wrap-around. I think in his case, standing and with some sort of sling, the anchoring of the set in the crook of his elbow was
…pivotal.
Last time I saw Paddy Moloney (a couple of months ago), he was playing a set with a wrapped bass reg. He is up and down like a yo-yo during a Chieftains set.
The W Rowsome set pictured above was modified when it arrived in America; you could tell since the modifier used broom-handle wood for the top section, along with generally crude work, not that Willie’s work wasn’t rough in spots already. Brad Angus replaced the brooms with proper ebony pieces.
Is Lewis still playing those? He was going to give them to Kevin R. Rowsome, that is. Kevin R, Rietmann that is, picked up the chanter Angus made for the set, that you see pictured there, for next to nothing; have been playing that stick for about 8 years now. Lotsa tunes! 
Kevin Rowsome had a spare Willie R B flat chanter lying around in a drawer or something.
The Taylors mostly used the bent-back bass; later examples take their cue from them. I think they invented the idea. There were some oddball older sets where the bass plugged into the stock before Kenna or whoever thought up the bass bar.
A lot of this grousing about painful straight bass bars could be cured with simply tying in the stock higher.