It has already been competing against fiat currencies and the least we can say is that it's a success.
No other currencies without a state to promote it, and basically force it on their citizens, made it through yet Bitcoin did it.
More and more people are buying it, people are valuing it more and more, close to 100k$ now when it worth nothing a few years ago.
That's quite a success to me and and I believe part of it's success is because Bitcoin is by nature deflationary.
No one would willingly buy an inflationary currency, the only reason they success is because they are forced by gouvernement.