Something like this could be implemented in a backward compatible way but is a tremendous burden to both code correctly and for full nodes to keep a complicated database of the fraction amounts on top of what they have.
For example you don't have to use the amount field anymore, just use the witness part. A witness version X (like 3) could do it by assigning the first witness item to be the fraction amount. In case of two 1.9 and 1.9 inputs the fractions go in the witness item and become 0.9+0.9=1.8 and the old part is still 1+1=2. Both nodes are happy.

The problem however is that the following statement is not correct: