edited/updated
A 3-piece Copeland on Ebay inspired me to post this. Which feature in a low whistles do you want to have the most?
Perfect tuning, easy reach, comfortable air requirements, medium’ish volume, and a tone fitting my preferences. And I don’t really want to compromise on any of those criteria, so don’t ask me to prioritize. 
Splitting a low whistle in three roughly equal segments makes it quite portable, actually a shorter pack than a standard pennywhistle.
Also, they’re plenty of hard bags available from flutes.
I have such one made by Yvon Le Coant out of Afr. blackwood, a lot like a flute. However, this takes a cork joint and, with it, a bulge of the wood plus an extra ferrule. Accordingly, this propels the whistle in flute prices…
With metal, I’d like to see how stable and secure it is: the fit of this lower section should be quite tight.
This from my experience of a horrible mishap: Alba sends me a new Low D. As an extra surprise, she makes it in three pieces, here get the prototype–whooopee! Great worksmanship, with the lower assembly machined in the aluminium tube thickness, and totally invisible when assembled. Good tuning, great sound, and so convenient! The next day, I just gave it a slight shake to swing off the head some spit clogging it… Of course, the lower part flew off, and got smashed bouncing on the tiled floor. 
It’s on the way for repair. You can be sure that, when it’s back, I’ll use beeswax to make this lower joint as tight as possible!
Now, to answer your question directly, Tak:
I’d rather have a low whistle either:
non-tunable or just with a sliding head (à la Howard).
or 3-piece, for portability.
The why is simple: if you want it tunable, it’s to play with others. Then it might as well be portable.
I still like the head to detach. It may be not to make it tunable, just carry the head around in a pocket to warm it up to in-tune/non-clogging temperature.
PS: I heard from a good source that Burkes low Ds used to be a three-piece split design. Anyone to confirm?
oops, make that “3-piece”. <----solved
Ach nein…where’s the poll? I put up a poll and it’s gone…I remember casting my own vote and it was there awhile ago..!?
Zoob, my Burke low-D AlPro is three pieces. The head seals to the body with 2 O-rings, and the body splits between the hands. The low-C is three pieces, but it splits between R2 and R3, which makes the reach easier. It’s still a bear to play, though.