When someone spends outputs that have a fraction of a satoshi, the transaction will appear to be invalid because it violates consensus rules. If you can send a fraction of a satoshi, you can also send 1.5 satoshi in an output.
Spending zero satoshi is backward-compatible. New amounts will be visible only by new clients, the old ones will see moving zero satoshis from some inputs to zero satoshis to some outputs. It is similar as in Segwit: if you run some old client, you see no signatures in Segwit inputs.
Unfortunately it's not backward-compatible. Let the new amounts be 1.9 and 1.9, the old will be 1 and 1. Adding the new amounts we have 3.8, the old ones see only 2. Let the new outputs be 3.1 and 0.7. What about the old outputs? We cannot put 3 and 0, the old ones can spend only 2. The new outputs diverge further and further from old ones. In fact old amounts become fake.
as you say
just having old nodes forget anything below a satoshi wont work.
leading to old nodes not relay these tx's as they are breaking the transaction value audit
but also
the 'change'(tx fee) which then turns into coinbase reward would also be unauditable
the auditing of all the change wont tally to the same amount as the coinbase fee reward and would void the whole block
which means it involves alot more cludgy code to redefine consensus than just having a new tx format that measures value in sub satoshi units.
