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To original question, then I'll go back and read what everybody else said:
My first and only CC was a Mfone 184 5U with the major 3rd 5th valve. I liked it so much that had I kept the NStar, I might have asked to have a "proper" 5th valve made for it, that didn't require all kinds of weird fingerings and nothing actually in tune when you got beyond two valve combinations.

Even thirty years ago - as a ‘feshunnul’, my ability to focus very low embouchure/air (as well as the low range response of affordable automatic tuning devices) were not what they are today.
Being decades better at focusing my own embouchure and air in that range – thus more sensitive to where the centers of pitch are in that range on a given instrument (and again: combined with the extremely improved low range affordable electronic tuning technology available now) these things have shown me that any five valve system just isn’t going to supply a complete array of close-enough-to-in-tune fingerings for all of the chromatic pitches in the range of an octave. (again: As many of us know, the pitch one step above the fundamental with the more common five-valve system - 5-2-3-4 - is wildly sharp…as sharp as – as an example – B natural played with 1-2-3 on a three-valve B-flat tuba.)
Again, some pitches may be judged to not be needed. I judge a couple to not be needed. I’m restating something (for the third time) which I should not be repeating again (ie. boring to subscribers), but composers and arrangers continue to extend the range of the tuba downward toward the fundamental range (into the bottom of the first overtone range) and those who actually listen to music are becoming more and more accustomed to dead-on/absolutely-in-tune musical sounds. ...and - after at least six decades of enhanced bass in recorded music - just about as sensitive to low-frequency tuning as they are to high-frequency tuning.
I own a wonderful C tuba - built in C -that plays stupid-easy in the low range. As with other instruments which I have chosen to keep for myself, it does a good job of making me sound as though I play better than I do and that I practice much more than I do. As with roughly 100% of C tubas which are made, it is a five-valve instrument. More and more often, I am encountering “low D“ in written music. My fourth slide moves very easily. That having been said, I find it extremely annoying to have to reach over there and frantically pull that slide out several inches to offer a competently-tuned “low D“.
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There is a local community band that is formal but isn’t “by-the-book” formal, and isn’t snooty (so I sit in with them at some rehearsals - from time-to-time - which are AFTER concerts and NOT right before concerts. Several of my friends play in that band, including the director) I just thought of one current (glaring) example of tons of low D’s in a piece of music - it’s just a community band arrangement of the “Jaws” theme (ie. the Tommy Johnson tuba solo given to other instruments). Seemingly, there are dozens of “low D’s”, and they pass by in that fast moving eighth note pattern bass line. D works out well on a 4-valve B-flat tuba (234), but not on a C tuba. That having been said, the constant “low E“ naturals - in the same fast-moving bass line - stink on a 4-valve B-flat tuba (unless compensating). ‘ just more championIng of the 4+2 system - were it offered on contrabass tubas.
...and yes: compensating B-flat tubas tend to tune all of the very low range pitches quite well all the way down to D-flat (with low C and low B natural stinking pretty badly, but - arguably - really not needed), but so many Americans reject those instruments for one or two reasons: [1] top-action [2] B-flat

Has anyone ever tried a quarter-tone valve?

This is a textbook example of the thing I was trying to explain above:
In the past (decades ago: when a four valve C tuba was just fine, and 1-2-4 was “just fine for ‘low F’ “), people put up with very mediocre intonation in pop music, and (as some old recordings tell is) “pretty good“ intonation was often tolerated in classical music.
Even though it can be easily argued that today’s pop and country music lack imagination, the intonation is completely fixed in just about everything, and that’s the situation to which people/patrons are accustomed today. Any out-of-tune playing in orchestra auditions (where tuba players‘ low range playing is closely scrutinized) likely disqualifies applicants.

pjv wrote: ↑Mon Aug 09, 2021 1:53 pm Has anyone ever tried a quarter-tone valve?

My Cerveny BBb has got a trigger at the 2nd valve slide (to operate with the left hand). That's the same function.

yep...
particularly if its as easy to operate as a valve

Estubist wrote: ↑Tue Aug 10, 2021 10:50 am

pjv wrote: ↑Mon Aug 09, 2021 1:53 pm Has anyone ever tried a quarter-tone valve?

My Cerveny BBb has got a trigger at the 2nd valve slide (to operate with the left hand). That's the same function.

bloke wrote: ↑Tue Aug 10, 2021 11:48 am yep...
particularly if its as easy to operate as a valve

Indeed, sir.

(I still want/am willing to pay for a bloke-installed 2nd valve trigger on my Symphonie to make a couple of notes easier. It only needs the paddle/linkage, as everything else is in place from the trigger installed for the previous owner.)