Bitcoin is already divided in to milli-satoshis (msats), which is 0.001 of a satoshi, as the base unit on Lightning Network. For comparison. 1 milli-satoshi is 0.00001 of a US cent.
Anyhow, I personally believe Bitcoin will never be a mainstream payment system, history has certainly shown us that Bitcoin is simply not that good when it's used as daily payment and we have far better options.
That's what Lightning Network should address. Instant and almost fee-less transaction which can be used for transactions which require immediate confirmation, such as the often talked about "buying a coffee with bitcoin". You only need to broadcast to the main chain and wait for confirmations when you close a channel, or if you want the extra security when making or receiving a large payment.
I'm curious as to what "far better options" you think we have.
People have been selling the idea of 'instant transactions' for quite a long time and yet there is no cryptocurrency out there that has instant transactions, bitcoin transactions take minutes, even hours sometimes. Even if you can have instant transactions and without fees, bitcoin would still be garbage as a payment option, why in the world would anyone accept Bitcoin in their business when the price can crash 20% in one day?