Imagine the following scenario (that could possibly occur in decades):

Bitcoin becomes widely adopted, its marketcap surpass the dollar's, and it become so valuable that even a single satoshi is worth more than, for example, a couple of pens, a bottle of water, etc.

In that case, payments for small amounts wouldn't be possible even with second layer solutions such as LN, because even a single satoshi would be more valuable than the price of the product. There would be a need for Bitcoin to be more divisible, for it to be broken down into even smaller parts.

Would such need to use smaller denomination units (smaller than satoshi) require a hard fork? Can someone shed some light into it?