The fourth valve (per usual) can certainly be tuned to play the two pitches a perfect fourth below the second and third partials much better in tune than a non-adjusted 1-3 valve combination, but the pitches a semitone below those two pitches (2-4) remain terribly sharp, and the common length of the fourth circuit is not particularly helpful for the extended low range at all, as far as filling in the chromatic gap.
It seems to me that - were a fourth circuit tuned to a tritone (augmented 4th), the two pitches which are an augmented 4th below the "open" second and third partials could be (nearly) spot on in tune, and then a first circuit - which maximizes slide length (such as on the old Holton 345 Bb 6/4 tubas) - could be pulled out to in tune for 1-3, 1-4, and 1-2-4.
2-3-4 is already fairly close to an in tune valve combination for a pitch, and 1-2-3-4 would be fairly close to in tune for another very low pitch, which would define that the very low range (though still not completely chromatic and still not perfect, but what is perfect?) would be a little bit more usable with only four non-compensating pistons - compared to the predominant (99.99999%) system.
Some of us are probably already playing the pair of perfect fourth pitches with 1-3 (while pulling the first slide out), and leaving the 4th slide always pulled out enough for the 2-4 pitches to be properly tuned (which is basically halfway towards the system suggested in the previous paragraphs).
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... Some of the rhetoric above might be a little bit awkward and difficult to read, but I don't quite know how to express what I did above without using the type of rhetoric I did and risking being inaccurate.

