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Ever since I learned about scales, I've practiced playing the C scale every day as follows:
Now, after learning another major scale pattern with four fingers and no open strings, I realised that this shape too can be moved around, if only I had practiced it with fingers 2-3-4 instead of 1-2-3. So my question is: Is there any reason to keep practicing this pattern with fingers 1-2-3? Would it be beneficial to move to 2-3-4?
It's good that you have realised patterns are moveable around the guitar fingerboard, so well done! There is more mileage in learning something like this at open position with fingers that leave the index free to play lower notes once you've left open strings.
Eventually, you may well leave open strings completely when soloing - which obviously uses all those scale notes (and sometimes more!), at which point you can play in any key you like - open strings are somewhat restricting, and controlling them, and applying vibrato aren't easy either.
You've learned a one octave scale, but there are more useful shapes, starting on the bottom and going up to the top string, meaning two octaves. Lots of tunes go above that top C, and below that bottom C in your scale, so it's a bit restrictive, without knowing the extra few notes. trouble is, if you start that 'C scale' on the bottom string open, you're effectively playing E Phrygian rather than C major!
Although it certainly can't hurt to be able to play it with 2-3-4 as well, I don't think it makes much sense to practice that. Yes, the 2-3-4 turns up in shifted versions, but these are different anyway because you also need the index finger where you'd have just empty strings in the C-major version. So better practise them right away in the shifted version.
The only situation where this would come handy is when you have a static bar with the index, and use the other fingers to play melodies. However, a bar generally makes the hand less flexible, so you don't want to do that unless you need the bar for a sustained chord. Then again if there's such a chord, you won't have all of 2-3-4 available, and therefore need to adapt the scale pattern you use for the melody anyway. So again not much you could translate from having practised C-major with 2-3-4 and empty strings.
