What's going to happen to Bitcoin?
Bitcoin as a medium of exchange
The recent rash of announcements of companies withdrawing support for Bitcoin payments is both totally expected, given the dynamics of the cryptocurrency, and in my opinion a harbinger of the end of Bitcoin as a payments system. More broadly, the combination of the validation timeframe for a given payment, the highly volatile BTC-to-fiat price, and the resulting contention for payment validation makes for an environment where it just doesn't make sense to buy things with Bitcoin, particularly if those things are relatively inexpensive.
On the consumer side, you are getting your goods in exchange for not just the traded value of your BTC, but also the opportunity cost you're sacrificing to use them today instead of holding them until tomorrow. For sellers, the trade is even worse - you need fiat currency to run your business and pay your bills, so you need to accept the transfer and convert it as quickly as possible. You therefore want to get it validated immediately, but this means paying more in miner fees. If it doesn't get validated fast enough, however, the price difference between the BTC transferred and the fiat price will be too wide. This situation makes Bitcoin untenable as a medium of exchange. In some ways, it's a victim of its own success: even if there wasn't a speculative surge in price, this issue would likely have still come up as more merchants joined the system, increasing validation times.
Bitcoin as a store of value
Bitcoin as a store of value is much more interesting. It shares many characteristics with gold: scarcity, liquidity, and no counter-party risk. Unlike gold, it has no threat from extraterrestrial mining. Also unlike gold, it is infinitely subdivisible. There is no obvious reason it would be tied to market performance, so it serves as a reasonable hedge. The mind share and brand it commands means that it already has quite a lot of stored value.
Assume Bitcoin fails entirely as a medium of exchange. Where can it go from here? Let's look more closely at gold as a comparison point. This is not a perfect match, because gold has some utility beyond being a store of value, such as jewelry and industrial applications, but it should provide a good order-of-magnitude estimate.
An estimated 187 kilotonnes of gold has been mined. As of today, the gold exchange rate is $43.38/g, or $43,381/kg. That means the world's supply of gold is worth about $8.1T. Of that, roughly 20% is attributed to private investment - that's about $1.6T.
Bitcoin has a fixed supply of 21M BTC. Let's assume that Bitcoin becomes as popular a store of value as gold, and thus has a total supply value of $1.6T. In that case, each BTC would be worth about $77,000. More realistically, it would split that market share with gold and other stores of value. Nevertheless, a price of $50,000 per BTC seems acceptable to me, and even $100,000/BTC doesn't seem wildly outrageous.
One implication is that, even if Bitcoin completely fails as a medium of exchange, it could still have quite a bit of headroom on the price due to its utility as a store of value. In that case, the prices would not be wholly speculative.