I've been thinking a little more on the fluidity of T-1-2-3 'across the board' fingerings when playing, for instance, Bach cello suites at pitch, and I hope I'm not going too OT with this side note.
Solo Bach requires a kind of fluidity and 'oneness' with the instrument which, in my opinion, really 'exposes' the classical musician to the audience. There's nowhere to hide: you need to control each note, each phrase, and bring out the architecture of the piece as a whole. It's a terrifying balancing act that demands that you are not thinking about any physical challenge, but instead are focusing on expressing deeper thoughts and emotions. The technique should never be in your mind.
This 'musical nirvana' aim while playing, which I found through Bach, is, at least for me, THE goal, and I would imagine this applies to all musicians in all genres.
Having more chordal shapes (like T-1-2-3 in the higher register) in one hand position allows us to really 'feel' the chords under our hands, like a pianist. With 1-2-4, we can't play a scale in any mode or key without shifting (without using open strings). I found having all the options right there under my hands in the thumb position really beneficial to achieving the fluidity of musical thought required for Bach.
It also reminded me of EB playing, and at first I wasn't sure why. Physically, thumb position DB and 1-2-3-4 EB are such different beasts! It finally struck me that the logic was the same, the patterns the same. Then I discovered that 1-2-3-4 fingerings on DB were a real option, and that they have been taught for many years.
While I adapted the 1-2-3-4 patterns and incorporated the logic into my existing 1-2-4 system, an EB player, I believe, could really benefit as a beginning DBist by seeking out a 1-2-3-4 teacher, (as difficult as that may be) as the scale patterns and logic will be exactly the same, and that fluidity which I spoke of would be naturally built in to their LH fingerings. They would not need in later years to re-apply thumb position logic for lower positions, because the same logic would apply all over the bass!