In reality I hold bitcoin, not dollars.
I think the answer is no. The age of the billionaire will not be replaced by the age of the trillionaire but by the thousandaire.
There are about 1800 billionaires in the world.
lets say having 1000 bitcoin would be equivalent of being a billionaire, that would mean we would need about 1,800,000 bitcoin just for those 1800 billionaires. that means there's about 19 million bitcoin left for those who own less than 1000 bitcoin.
This actually does seem plausible. It seems to match quite well with the zipf distribution of wealth (the rich always hold much more in proportion to the non-rich, bitcoin is not likely to change that).
this would also mean that for this to happen, 1 bitcoin needs to be worth a million dollars (in current days dollars). Which is entirely possible in the long term.
i would be surprised if you could buy 10 bitcoin for a million by 2030.