Techcrunch reviews the various issues surrounding both hardware wallets ("cold storage") and internet-connected, software wallets ("hot storage").
One currency, one wallet: this is close to the reality today when you move past the top four or five currencies. You will find some wallets that are supporting up to 10 currencies (and I am not referring to ERC20/ICO tokens). But there are hundreds of chains and forks out there, each with their light wallet. One wallet for NEO, one for MONERO, one for Ripple and so on. There is no solution that can help you host all the main currencies at once (even the top 30), in particular on mobile. This is like getting a different browser for every site, or a different remote control for every TV channel.
https://techcrunch.com/2018/02/01/the-sad-state-of-crypto-custody/