Again, this is not a suggestion for chaining bitcoin. That is in the title.
Rather it is a question about what could be possible, and what couldn't be possible. The general question is, could the block list be/have been implemented in a way that didn't store the full transactions in the list?
The answer could very well be, no.
But your saying, "The public has to see the transactions to verify them." Does not make that so.
When you are done parsing the block list, you will have the minimal set of valid and unspent out-points.
In this context it means a set of unspent out-point hashes. These hashes do not contain bitcoin quantity information.
I know what a balance sheet is. I was there for that discussion. I supported their possible utility.
This is different. The balance sheet was a way of rolling up known transactions that already exist in the block list. This is an exploration of never putting transactions into the block list at all.
It may still be a FAIL, but the question is not can you think of ways this might fail. It's can we prove that it must fail.
If you want to provide more privacy you could always...
Feel free to make your own suggestions in your own thread, but your suggestion didn't meet any of the stated goals of this exploration.