Do you agree with this statement?
Let's say bitcoin price is 1 million dollars (since you said even when it becomes too valuable), do you think that people are still using fiat at that time? Maybe, maybe not? Maybe the two things just continued to co-exist but surely fiat has become worthless to those that have migrated to using bitcoins. At that point, merchants are obviously already accepting bitcoins and people are more into buying and ordering things online.
Fiat will always be precious to those that use it and don't know how to use bitcoins. And bitcoins will always be precious to those that are already using it. This is where the digital divide comes in. Basically what it says is that there's a technological and/or economical gap between the members of the society. Ones that have an access to the Internet, and one that doesn't. The former will eventually adopt to using bitcoins (assuming that bitcoin continues to grow) while the latter will just use fiat until they finally have access to the Internet.