This is a good try at a theory of when you can use weak isolation. But as stated, I believe it is false. If the invariant is A+B=C, I think this sequence is permitted by READ COMMITTED:
T1: read A=1
T2: read B=1
T2: write A=2
T2: write C=3
T2: commit
T1: write B=10
T1: write C=11
T1: commit
Now A=2, B=10, C=11
More to the point, invariants aren't always local to a row, and people don't usually even fully articulate them.
> There is no need to pay the huge performance price of serializing those transactions with all the rest of transactions in the system
Serializable execution can be made very very fast when there aren't actually a lot of conflicts. And then when there are you can do the hard work of trying to prove that something weaker will work. The failure mode in the other direction is silent corruption of your data.