Thus, it might seem a bad idea to allow unenforceable amounts
We have the same in euros: most shops reject 1 and 2 cent coins, and yet most prices end on 9 cents.And this was not about payments but about forwarding fees. Even if you can see an utility for payments too (pay-per-call on an API for example).
Entire cents, currently worty far more than 100 satoshi, are lost due to rounding. And nobody cares 
Why would anyone care about possibly losing a fraction of a satoshi due to rounding?
Again, not comparable : my point that these tiny amounts may become valuable in a fraction of seconds. That is again true for a forwarding node or a payee for an autonomous service.Why would anyone care about possibly losing a fraction of a satoshi due to rounding?
OR for example, the possbility of a more than 6 digit per Bitcoin world. Instead of breaking Bitcoin's social contract by adding more decimal places onchain, do it in L2. 
Absolutely, I think the need for those tiny amounts is already present today, and it might be even more with a price increase !