This is commonly a argument for having drugs illegal too. "If we hunt them down, eventually there will be no one left"
What we know now, is that making something illegal, could make it stronger. If Bitcoin becomes illegal in most country, would the price go up or down? Suddenly there is a black market, and opens up a whole other can of worms, so governments might not be able to simply outlaw it.
It's not as though drugs became more popular because they became illegal. Prices may have gone up because they were harder to obtain and there's less competition. Demand was still there because.. well people like doing drugs or are addicted to them.
With Bitcoin, why would a business risk legal action to accept it? There's very little incentive as far as I can tell.
If bitcoins were illegal then I imagine they would probably only be used in illegal transactions.
This is not exactly a completely relevant example, but Colorado did see a decrease in teen marijuana use after marijuana was legalized recreationally (granted, it has also recently seen a decrease in teen heroin use, so the legal status may not be directly causal, but I find it interesting nonetheless):
https://www.washingtonpost.com/news/wonk/wp/2017/12/11/follo...
Regarding Bitcoin, one incentive might be positive press coverage - a PR move, so to say, such as when APMEX, the popular online precious metals exchange began accepting Bitcoin in late 2017:
https://www.coindesk.com/major-gold-dealer-apmex-begins-acce...
Many of these cryptocurrencies have non-profit foundations that push for adoption by getting ad-space at major events and pushing for the acceptance of cryptocurrencies in certain companies. Litecoin has the 'Litecoin Foundation' and they managed to get advertising for Litecoin in some UFC events. More often than not, I think partnerships like these make for good PR for both companies involved - here's a piece on why the Litecoin Foundation thought that this particular partnership was useful:
Whereas, a currency used by 0.1% of your friends / neighbors is totally useless.
These reasons make it 1) easier to suppress a currency 2) harder to suppress drugs.
Using something as a store of value has much less of a scale requirement. You only need a few people that will be willing to exchange your Bitcoin into something else in order for it to work as savings / an investment. Whereas a currency requires multiple places where you buy goods to accept it. Moreover, those places only really have a reason to accept a currency if multiple customers would use that currency.
Perhaps this is somewhat pedantic, but I think it's more accurate to say that there's a black market for drugs because governments have passed laws to make certain drugs illegal and some groups of people have accepted the risks that come with supplying the demand for this particular market in order to make a profit.
> On the other hand, people only like receiving cryptographic tokens on the assumption that they will be able to exchange them for something in future
It may not be exactly this simple, although this is mostly true. There are those out there that purchase cryptocurrencies to make foreign financial transactions in a way that may be considerably more difficult with their country's accepted currency. This doesn't necessarily have to be an exchange, it could simply be sending said cryptocurrency to a wallet of a relative in a foreign country.