If you can make it sound good without injuring yourself and if it makes you play things that are impossible or much harder with 124 I see no reason not to use it and extend your basic Simandl or Rabbath technique.
This is basically how I feel about it as well. Certainly, with enough right hand control, a high level of left hand facility, and diligence, one can successfully play many passages which I choose to execute with low thumb position/four finger technique/pivots for. But often I find that, even when executed perfectly, these fingerings do limit resonance (especially in things like Bach cello suites) and/or make it more challenging to convey certain musical gestures convincingly. Those factors are often equally as important as technical ease in my decisions to use certain techniques.
Although 1234 is not necessary, it might be a good idea to introduce it earlier in pedagogy. Understanding the concept, its strengths and shortcomings and especially training your 3rd finger for power and independence early can't hurt. For me, it is less a special trick, but one of many elements , to understanding what works on double-bass bass, why and how.
1234 without pivot and solid shifting won't work.
134 and 123 need different hand shapes than 124.
I love how you put this, and absolutely agree. A big part of my exploration of these techniques has come down to, over time, distilling my understanding of the mechanics of the hand and the mechanics of the bass and how the two intersect. To explore any new idea in technique, provided that it is done safely and carefully (or if it is in an inherently unsafe approach, then very minimally and only to the extent that we can gain some understanding of what about it doesn't work so that we can then avoid it in other aspects of our playing), is to explore different ways of using the hand. If we are always critical, aware, and inquisitive, this then informs our technique in a way that strictly observing only one way of playing can never do. I very rarely utilize my third finger without also including a pivot--usually, 124 with a pivot will accomplish what my third finger would just as comfortably, but every now and then using my third finger enables me to make that pivot smaller and more precise instead of having swing far enough to get my second finger where it would need to go.
Though, I kind of agree with what damonsmith writes, as I feel the bass 'wants me' to learn basics well enough and only then delve to experiment with more advanced techniques, and it is important to say it is so. But still, I like to peek ahead, because if I know what's coming, I can focus. Knowledge doesn't mean it will automatically be misused. Even the time lost this way has its merit, IMO.
I like the idea that time lost to premature exploration can still have value--I feel the same about my own work. In an effort to try and catch up and audition for things like All-State orchestra, colleges, etc, I was exploring repertoire much too difficult for my own capabilities very soon after starting to play (Bottesini and Vanhal concertos, Bach suites, excerpts like Mozart 35 and 40 etc). Though I wouldn't articularly recommend that course of action to a beginner, I actually am glad I did it. I couldn't play those things well by my standards today and my fundamentals were fairly inconsistent, but given that I started late on the instrument I think forcing myself to work up the ability to even sort of hack my way through that material gave me a certain level of facility to get around the instrument and actually helped me minimize many left hand technique problems that I might have developed working on easier material without guidance, because getting any semblance of success in repertoire of that difficulty demands a certain amount of healthy approach in the left hand. Of course, the bow was another story... Harder to learn that one from the internet, at least at that time without the Discover Double Bass etc resources that exist now. But once I got with a teacher and rebuilt my fundamentals over the course of a year or two, the jumpstart I had on the repertoire from my early self-taught exploration really helped me get a much firmer handle on both those fundamentals and on that music. It's not a path I would recommend, but I don't regret it as it taught me a lot.
I can tell from experience of myself and my students that the idea 'bass guitarists all play 1-2-3-4' that keeps popping up here is not exactly true. In reality, it's more similar to DB: the player looks for healthy, effortless aproach, and there is never really just one way.
Yes, bass guitar certainly can use 1234 in all positions, but even before I started on double bass I often would go for the the whole step span in the lowest positions. It just was more comfortable and I realized pretty early on that comfortable was 1) healthy and 2) easy, which translated to speed and accuracy much faster than anything else.