Bitcoin is, in a way, backed by the value that it brings as a currency-- privacy and anonymity. We can argue whether that value is $10 per BTC, but I also don't think any reasonable person thinks that it is zero.

No, in fact, plenty of reasonable people do believe it is zero, and you cannot nerd your way out of that fact.

But that's not reasonable. Its just ignoring the privacy/anonymity value of BTC. Again, we can argue about the monetary value as compared to dollars, (especially given the tradeoffs-- i.e., convertibility to established currency, places to spend, etc) but that's real, practical value. You can't simply ignore it.

Sure it's reasonable. I think bitcoins have zero value. I recognize that there may be people out there who are willing to pay real dollars for it right now, but I think that in the long run, no such people will exist. Hence, I place its value at zero.

Bitcoins don't have to be tradable to dollars to represent nonzero value. Their utility is in and of itself valuable. It might not have value to you, but that's different than suggesting that it has no value at all.

I fail to see how their "anonymity" has value when it cannot be exchanged for real currency.

Currency is a placeholder for value. So long as I can exchange bitcoins for value, they will function as a currency. The design of bitcoin makes it very difficult for governments to make such a scenario impossible (or even difficult). For that reason alone, bitcoins will remain valuable, if for nothing other than goods or services that governments don't like.

People who participate in illegal trade (such as drugs, guns, prostitution, etc.) still need most of their purchases to be in the legal economy. Hence, illegal trade still uses real currency.

I couldn't care less about the privacy/anonymity of BTC if the market falls out and my BTC wallet ~ $0. At that point no government will come to my aid because, hey, I invested in something that has no value.

As I mentioned above, Bitcoins value relative to the dollar is irrelevant, because its value is found in its utility. So long as there are goods and services to purchase with Bitcoin (and it seems very difficult for a government to stop such services from existing), the utility of the currency remains valuable, regardless of its exchange rate to the dollar.

EDIT: The fact that government would have a very difficult time shutting down the Bitcoin economy is yet another example of its utility and value.

Utility for what. If things have real, actual value, then they can be exchanged for dollars, even if it's only on the black market. We don't mean there has to be an official exchange rate between bitcoins and dollars. We mean there has to be someone willing to say "I'll give you X USD for Y bitcoins" even if that's just under the table. If no one is willing to do that, then bitcoins have no value.

What I, and others, are saying is that in the future, no such people will exist. Our prediction is that the current bitcoin economy is transient and will eventually vanish. Hence, we say bitcoins have no value. It's similar to saying that a particular stock has no value if you think that that particular company will collapse.

*there has to be someone willing to say "I'll give you X USD for Y bitcoins"

Not really. They have to be willing to say "I'll give you X thing that you value in exchange for Y bitcoins." The entire point is that the design of bitcoin makes that scenario likely to always be true precisely because it is nearly impossible to stop. As I said above, the very fact that it represents a system that is very difficult for state actors to attack ensures that it will almost certainly be used for exchanging goods and services that governments would rather not exist. Not a terribly noble future, perhaps, but certainly one that ensures bitcoins have value.

If people are willing to trade goods for it, then someone will be willing to trade dollars for it (or yen, euros, or any established currency).

For a reason that I am unaware of, you seem to think that just because something can be traded it will be traded. That's not true. People tend to only trade things that are readily exchangeable in the larger economy - things that have value.