Countries which make the transition to high income (e.g. Japan), do experience curves like this, which is what produces this false impression. However, as a whole, the high income countries grow faster than the middle/low income countries, getting further apart rather than closer, and the overwhelming majority of low and middle income countries do not experience a transition to becoming high income countries.
Since 1960, there are three main categories of countries that have succeeded at this task: European (e.g. Czechia), East Asian (e.g. Japan), and oil-rich (e.g. Saudi Arabia). The only exceptions are Puerto Rico (if you want to count it), Israel, and Singapore, the latter two of which are basically European and East Asian culturally.
If you a nation does become rich, the log of its GDP follows an S-curve as it does so; but most nations don't become rich.
Countries which make the transition to high income (e.g. Japan), do experience curves like this, which is what produces this false impression. However, as a whole, the high income countries grow faster than the middle/low income countries, getting further apart rather than closer, and the overwhelming majority of low and middle income countries do not experience a transition to becoming high income countries.
Since 1960, there are three main categories of countries that have succeeded at this task: European (e.g. Czechia), East Asian (e.g. Japan), and oil-rich (e.g. Saudi Arabia). The only exceptions are Puerto Rico (if you want to count it), Israel, and Singapore, the latter two of which are basically European and East Asian culturally.
If you a nation does become rich, the log of its GDP follows an S-curve as it does so; but most nations don't become rich.