If you look the maximum amount of Bitcoin that can be mined that is 21,000,000, do you think it is enough to overtake any currency which can be printed many times? Of course not even if the price of Satoshis is way up it is not enough to be distributed to all of us living in the Earth.
No one should see Bitcoin as a replacement of fiat currencies where the entire world population, or a big chunk of it, will jump into Bitcoin and start using it. So in that regard, there is no point into comparing the limited coin cap of Bitcoin with the unlimited fiat supply. Bitcoin is nothing more than an alternative. If we ever get to a point where 1% of the world population is using Bitcoin in one way or another, then it can be seen as a massive milestone.
In combination with a higher going price, although there are no guarantees that the price will really increase much higher than is the case right now, the number of available coins will be sufficient enough to serve all its users. The higher the price will go, the lower the amounts will be that people can afford, and thus, the more coins that can be spread towards a larger user base.