It's not all about gain; properly done they can be quieter while also hearing very well. If one's expectation is to toss away their tuner forever while listening to angels sing the premise of a bazooka probably isn't for them.
Actually the original purpose was wider operating bandwidth, not gain or low noise on receive. All the
designs I've seen (and the ones I've used) included a correction for the velocity factor of the coax: it
applies to the length of the coax stub, not the overall length of the antenna. That's why, in this
variant, the coax stub extends about 2/3 the length of the antenna and the rest is made from twinlead
to form a fatter element.
Commercial variants such as the "Snyder Dipole" have been patented on the premise of wider bandwidth
by using 25 ohm coax. Basically the two quarter wave coax stubs provide some reactance compensation
with a change in frequency - just like connecting a parallel tuned circuit across the feedpoint. The
type with the crossed connections puts the two stubs in parallel, which gives slightly better bandwidth
than in series (the version where the coax center conductor is uncut at the feedpoint.)
But it is still a dipole, and will have the same gain and pattern as any other dipole (minus the losses in
the coax stubs.)
Low noise? There is no way it can recognize which bits of RF are noise and which are signal, so it will
pick up the same amount of noise from the ether. As W8JI documents on his web site, precipitation
static happens to insulated antennas as well as bare ones whether they have a DC ground or not.
The only noise reduction I would expect to see is that due to a difference in pickup via the feedline
when the antenna is changed (which would be eliminated by a proper balun anyway) or the overall
drop in all signals due to stub losses.