Money’s value is based on the shared delusion of millions that it is valuable. Bitcoin’s value might “go to zero”, when most of the people that today believe it is valuable stop believing that.
People may stop believing that Bitcoin has value if their government bans it. While one government bans it, an oppositional organization or another government may endorse it. Some people might think that when a government bans it, this should be understood as the government perceiving it as a threat and assign more value to it. So even if “all governments ban it at the same time”, it might continue to enjoy some value.
If a catastrophic vulnerability were discovered in the Bitcoin protocol that might shake some people’s belief in the value of Bitcoin. It might also boost other people’s confidence if the problem is resolved quickly.
We have seen several other cryptocurrencies have catastrophic failures, and yet, their value has not collapsed to zero. For some, the notoriety even increased the exchange rate at least temporarily.
Even if many lose confidence in Bitcoin, it might still solve issues for a smaller community or retain some unshaken supporters. In the end, value of money is an individual perception and even if many change their perceptions, there might be some that buck the trend. There is an old adage among Bitcoiners responding to your very question in the vein of “Bitcoin can’t go to zero, because I’d buy all of them at $0.01.”, to which another responds “Oh, but I would buy all of them at $0.02”.
So, while it is possible for the exchange rate of Bitcoin to drop precipitously, it seems unlikely to go all the way to zero.