When one Satoshi is worth $1, Bitcoin will no longer be adequate for regular payments

It's pretty clear where Bitcoin is headed. Everything seems to be going smoothly so far. I remember sitting in a baseball stadium with my friends in 2014 and saying "we are so lucky. we are probably the only ones in this stadium who have even heard of Bitcoin". Then practically overnight at the end of 2017 Bitcoin became recognised in every household. Now an entire country accepts it as legal tender.

In 2013 I created a simple exponential model for information dissemination and plotted it on a graph just because I was interested in how this Bitcoin rollout is going to look. The result, when you plot "number of people who understand Bitcoin" over time you get a sigmoid function. It's very slow to start (10,000 BTC for a pizza), then rapidly scales up through a period of adoption (Bitcoin suddenly on every news channel), then equally slowly starts to reach it's equilibrium at the top (we're not there yet).

Say it takes on average 3 years of hearing about Bitcoin for a person to switch from "I've heard of this" to "I will use this". Then 3 years after the end of 2017 (when suddenly you could expect people to have heard of Bitcoin) is the end of 2020. So let's use that as the zero point in the sigmoid curve of adoption: we are currently halfway through the adoption process.

$14 in July 2011 to September 2021 is 3270x. So given that we're halfway and the sigmoid function is symmetrical, in 2031 we are another 3270x. About $150 million per Bitcoin, or $1.5 per Satoshi. Only then will we start to see equilibriums reached, lower volatility, etc.

This is all just basic maths and modelling.

So I price one sat at $1.5 (today's dollars).

The only question is: will there be a hardfork to extend the decimal places or will we have to rely on some other mechanism for making more granular payments?