They work by having every coin backed 1:1 with some real-world asset (USD, gold, securities, etc.) in conjunction with a transparent Proof-of-Reserves.
This will allow users to keep money in crypto without risk of volatility and transact as needed without the permission of a bank.
3. Governments will shut it down.
Governments interfering is a real risk and they need only mention words like "terrorism", "money laundering", or "illegal activity" to step in.
Exchanges are the weakest point of failure right now because they are centralized and run by a single company.
I think we will see the introduction of decentralized exchanges that operate as decentralized applications.
This will make them incredibly difficult to shut down - just look at P2P file sharing like BitTorrent.
Additionally, it makes banning specific coins equally difficult (ex: privacy/anonymous coins like Monero) since they can be exchanged for with any other cryptocurrency.
4. There are too many different coins.
Every (legitimate) cryptocurrency has a team, mission, and roadmap behind it. Similar to a startup building a service or app that addresses a specific market of users (ex: Monero or ZCASH for transacting anonymously, Ethereum for apps and contracts, LiteCoin for fast/cheap transactions).
Exchange between cryptos will also become instant and easy for users, built right into wallet software, enabled by technologies like Atomic Swaps and ShapeShift.
This could enable a model where users store their money in a Price-Stable cryptocurrency (see #2 above) and then convert it when they need to use it.
The alternative is that one coin is able to solve every major use case "well enough" that it becomes the dominant player.
5. It's bad for the environment.
Proof-of-Work systems like the one used by Bitcoin have been criticized for "wasting" energy.
Proof-of-Work's role is to prevent attacks from malicious actors by requiring them to burn energy and therefore making it uneconomical to do so.
There is an alternative called Proof-of-stake that accomplishes the same thing, except it asks miners to provide a monetary stake instead of energy.
Proof-of-stake is already being used in various cryptocurrencies (DASH, NEO, etc.) with success and has been proposed for Ethereum.
6. It's not user friendly.
It's still way too difficult for regular users to store their money securely, or send money without losing your coins if you mess something up.
Wallet software, hardware, and services like Coinbase will continue to improve - eventually it should be as fool proof as sending money with PayPal
Wallets will also integrate directly into apps and browsers - enabling developers to interact with users' funds (request or send a payment, setup a smart contract, etc.)