So, funny story, in the beginning of 2022, I came up with the exact same scheme discussed in this thread. ...
I've spent the last year implementing it, so just 10 years after the OP, you can finally try it out!
The binary, written in Rust, is called
ord, and the code is on GitHub at
https://github.com/casey/ord.
Sounds like a fun project, but I don't think the idea has any practical use
because there is no real association between the satoshis in the inputs and the satoshis in the outputs.
I'm happy to admit that I was proven wrong, but I'm still waiting for a
practical use. I'm not saying that there is no practical use, just that I am too closed-minded to come up with one.

Curious to know how you were proven wrong. I also was just wondering the same thing. Is there any