The way it works with WhatsApp and Signal is that your key is generated on your phone and never ever leaves it. The web client actually establishes a connection to your phone and routes all messages over it.
Now, the Axolotl ratchet protocol does support encrypting messages to multiple keys (it's what they use for group chats), but doing it properly requires time and effort in order to remain secure.
wire.com/privacy for security whitepaper.
For me, multi device support is not important since I have my phone with me all the time, and if I'm on my laptop there's the web client.
Apparently XMPP with Conversations + OMEMO provides secure multi device support, haven't tried it though and I'm not sure if I could get any of my non-tech friends to use it.