If there's no support network for your bitcoins, their value is 0, exactly. Even if you assume people stop caring for shiny imputrescible metals, its intrinsic property (of being shiny and imputrescible) pretty much ensures there will always be some demand for gold, and thus it will keep a non-zero price. Possibly low, but not actually zero.
It matters a lot of part of the reason to invest in them is as a hedge against general collapse of social institutions.
If you mean the former, then yes, gold is a good hedge. But if you mean the latter, then I would argue Bitcoin beats gold 100x.
The world economy has never collapsed, and if it did, it would be equivalent to the first option.
If you mean a short-term market downturn like the one that occurred with the ~2009 financial crisis, why would I even bother to hedge against that—and, if I did, why would I use an asset with high volatility to hedge against short-term market movement?
During such times you need an asset whose value will be greater than 0.
Or 2,000 years:
"the researchers look at pay for a Roman legionary, in the era of Emperor Augustus (27 B.C.-14 A.D.), who was paid a salary equivalent to 2.31 ounces of gold. A centurion was paid a salary equivalent to 38.58 ounces of gold.
Compared to modern US Army salaries, a private is making 20% more than the legionary, and a captain is making 30% less than the centurion" [1].
A counterpoint can be found in silver, where unexpected Spanish silver production in the New World prompted inflation around the world [2][3].
TL; DR For historical reasons, gold is grandfathered into our collective consciousness.
[1] http://www.mining.com/what-a-roman-centurions-pay-says-about...
[2] https://www.theguardian.com/cities/2016/mar/21/story-of-citi...