But paying sub-statoshi amounts on-chain makes no sense as long as the minimum fee is 111 sat.
Maybe the dust amount value of thousands of satoshi for on-chain transactions is also something to be taken into account.
So while satoshi subunits are OK for LN, they aren't practical yet for on-chain, hence there's no rush
yet.
$0.01 is close to worthless, so I don't think it would matter if 1 satoshi became worth more than $0.01.
The current 0.01$ is... just for now. If we think that a bull run increases the price about 20x and we tend to have 4-year cycles, in 4-8 years this may become a problem to be seriously discussed and maybe handled too.
And maybe the fact LN uses such subunits will make this problem get properly into attention even earlier.