Millisatoshi (msat), or 0.001 of a satoshi, is already the base unit on the Lightning Network. For one millisatoshi to equal one US cent, then one bitcoin would have to equal one billion dollars, which would give bitcoin (assuming all 21 million had been mined) a marketcap of 21 quadrillion dollars. This is more than global broad money, all the global real estate, all the money globally in stock markets, and all the global derivative markets combined, by a factor of 10. It will be a long, long time before we will need to subdivide further than one millisatoshi.

The question, then, is whether you think Lightning Network will become the main way in which people exchange bitcoin, and how often you think people will be closing channels. Since millisatoshi can't be broadcast to the main chain, if there is an discrepancy when a channel closes, then the value is simply floored to the nearest satoshi. At present, that means losing out on fractions of a cent, but in the hypothetical situation above, you could lose up to $10 on closing a channel.