Ooh, yeah that would be great.
That behavior sort of came up organically a few times when I played just due to random chance.
The only thing I'd say to be careful of is making it too puzzly. I think that's definitely one way you could go with it, but there's a lot of space between puzzle with single solution and problem that you have to solve, and your game's mechanics are already quite a mind-screw.
There's something to be said for just being able to play around and experiment to learn the systems, and I think I would have gotten frustrated if the early fights were more puzzly (not saying there's no space for that, but the breathing room was nice).
For reference, I acted somewhat randomly for the first several fight, discovered what seemed like a dominant strategy for the next couple, then mostly understood the mechanics once you gave me the power to change my digit.
The fact that I then had to experiment in the boss fight, but still had room to make mistakes, felt really really good. Like an actual long battle, where I was figuring stuff out as I went. It had a little story to it for me.
So yeah, while I agree, I think just be careful if you move forward with Single Digit of how narrow the solution space is in fights!