I'm 100% convinced cryptocurrencies will continue to vigorously grow for many years to come because they fulfill a huge need. There has been talk about micropayments, deterrence against DDos attacks, and decentralized digital money for as long as I have been using the Internet (since 1992) but until Bitcoin came along, there was nothing like Bitcoin, a trustless peer-to-peer currency, in existence. Although I think Bitcoin will grow for some time, it has already clearly begun to lose market share as competition has been stiffening and as the inherent limitations of Bitcoin's underlying technology have become painfully obvious. The 17 euro fee for transferring a little over half a bitcoin a few days ago was painful, particularly because it took a couple of hours to confirm. This is unacceptable.
Segregated Witness will not help for long at the rate Bitcoin is currently growing. SegWit will only increase block capacity by a factor of 1.7. Increasing the block size requires a hard fork. Also, mining larger blocks will be more expensive putting more power into the hands of runners of full nodes, leading to more centralization, which is against the original premise of Bitcoin. Ultimately, no increase in block size will be sufficient for the projected growth of Bitcoin in the future. There is no way for Bitcoin to grow and to even retain its current share of the cryptocurrency market let alone capture any significant share of the remittance market, for instance, without implementing off-chain solutions. With the SegWit/Block size limit controversy beginning to look very hard to find a solution to, I can only imagine the damage the current situation will cause Bitcoin even in the medium term.
No blockchain is immune to the scaling problem. Perhaps other types of solutions are needed for implementing a single trustless and private cryptocurrency. A couple of weeks ago I ran into articles about IOTA, a distributed ledger not based on a blockchain but a directed acyclic graph called the Tangle. Here's an article about the technology that makes IOTA tick. IOTA promises to be infinitely scalable, without transfer fees thus enabling nano payments, and quantum resistant. One of its main use cases will be machine-to-machine transactions (value transfer using IOTA tokens and smart contracts). This is quite new to me so I will have to delve into the topic for some time to understand it.