What would happen if Bitcoin become the dominant, reserve currency on the market?

Nothing.

Apart politicians would not be able to steal purchasing power from the fiat currencies held by the working people using the printing presses to print money for themselves and their supporters.
Without the printing presses, they would be forced to tax or borrow from the public.
But if the tax they will be hated and if the borrow they will be hit immediately by rising interest rates. The current interest rates are unsustainable without the Fed. running the printing presses at full speed to keep them at this low levels.
It would be the end of profligate spending by politicians to keep people on the dole (to vote for them), to finance stupid projects, to make stupid wars, etc.

There will be higher interest rates, so people will be interested in saving more, delaying consumption, investing only in really high return projects (no stupid solar panels, windmills, and likes).
Without money the government will not be able to finance the War on Drugs and other stupid wars like the War on Terror.
Instead of focusing on winning hearts and minds they will stay real and will focus on splatting skulls and chests (cheaper, faster, surest).

Prices for stuff like homes and other will fall as interest rates will raise. People will pay a house full in cash or with a small loan. They will not be serf for 30 years to the bank.

Just little things like these, nothing more.