Why would people begin to accept other currencies? Without an economy backing them up, they'd be useless. It's like all these crappy little news sites that pop up on the web - it's trivial for them to be setup, so why not do it? But people don't go to them, because they aren't reliable, or just that the bigger news sources are better.
Put another way, there are too many crappy little news sites, and nothing controlling their proliferation. People read their news where they think they can trust it. Or where the brand is strong.
Which gets back to the original question. If there is no control on the number of crytocurrencies, will we end up with masses of "crappy little news site" equivalents? Or will something (bitcoin or something better) float to the top and keep people engaged?
Maybe bitcoin just becomes a branding exercise. Battling to stay on top of a morass of competition. First mover might help, and might keep it entrenched for a while. Think Microsoft. But it will constantly be under assault if people can come up with something better. Actually that would be a good thing. Good money driving out the less good.
But since there is no central ownership (or so I'm told) who will fund the branding? Maybe the users in an attempt to protect the utility. But equally possible is a competitor currency driven by business people and cryptobankers. Who know how to make it work in a bigger piece of the economy. How to market it. How to work on PR. How to brand it, essentially.
Claiming to know the answer to all this is not really credible. We can only speculate on the outcomes.