With a trillion dollar market cap and an ever-growing industry, it is quite possible that in the near future, cryptocurrency could play a major role in the world market, especially when global adoption is realized. But for now, it wouldn't be the case because as it stands, cryptocurrencies and bitcoin adjacently is still in its infant state. A lot of improvements within the infrastructure and also within the industry itself must be changed before it could take on the world market. For instance, it's heavy reliance on its deflationary nature makes it not fit for long-term usage, as the developers would have to choose between high value, or more customers. Scams are also rampant in this industry, but so is anywhere else, the problem is that this is debilitating for an industry as recent as the cryptocurrency world.
I do not think that even at a much higher adoption rate, it will not "lead" the worlds market, it will be a good alternative and it will be used by many people but I do not think that it will be leading anything at all.
It will probably be something normal and it will probably be used by a lot of people, tens of millions of people already owns or owned bitcoin before, maybe it will reach a billion one day, not number of people who holds it, but at one point ever had it, and if that's reached that would be awesome. But the whole world is using fiat now, and I think it will continue to be like that for a long time and it would not be that easy to stop doing that anytime soon.
Fiat will never be extinct and will continue to be the only one official currency in the whole world, leaving bitcoin as next to fiat since it’s never intended to compete with fiat in the first place. So even if the adoption rate is very high, you cannot expect that people will shift easily and leave fiat as easy as that. Although I believe that bitcoin has really that huge potentials to rule the market, but I don’t think all countries government will root for it.