There is the theory first described by Hal Finney that if an alt currency supplants bitcoin (in which Bitcoin's value goes down as coins are sod for transfer to another) then that is something that too can be repeated over and over, and thus crypto currencies lose their ability to be a good store of value.
So that happening harms, over the long term, not just bitcoin but all crypto currencies.
But Bitcoin is a proof-of-work (POW) based crypto currency, and thus it is susceptible to a 51% attack. Thus it needs a sufficient level of hashing for the network to be protected. This is what differentiates bitcoin from competing POW-based crypto coins which have a hashing capacity just a tiny fraction of Bitcoin's.
But there still could be multiple successes, since all that needs to remain protected from a 51% is sufficient hashing capacity and there might multiple POW currencies with a sufficient level.
At this moment, Litecoin may not yet have a sufficient level but it is the closest to Bitcoin to reaching that state.