Why won't Alexa stream different songs to different rooms simultaneously from Amazon Music?

That all depends on how the music service handles multiple sessions. Amazon isn't the only one to handle it this way... where initiating play through the Sonos controller allows multiple streams to different speakers.

I believe Spotify works the same way... but if you start streaming through the Spotify app on your phone via Spotify Connect, you're likely to only get one stream as well, just like when initiating Amazon Music via Alexa. I don't have Spotify, so I can't verify these claims first-hand, but I believe that's how it works based on others posting here.

Thanks for your response. I have been researching online and it appears the only way around this is to pay for the Family Unlimited Music Subscription with Amazon.....for £149! This is a major disappointment and means I must revert to using the app again.

I really do think Sonos have made a grave error teaming up with Amazon. They should have retained their independence, now Amazon will push all its proprietary services onto the Sonos community. I expect it is only a matter of time before Amazon end up owning Sonos, then watch as Google Music, Apple Music and Spotify start to fall off the supported services list.

They've teamed up with Amazon first. Probably because Amazon was willing to pry off a team of engineers to make it happen. But Sonos has indicated that they want to team up with other people, like Google, and Apple as well.

It might be worth reading this thread:

https://en.community.sonos.com/announcements-228985/exciting-partnerships-in-the-queue-6791309

Not only do they want to team up with Google and Apple, they actually have. Nothing indicates Sonos is not still maintaining independence with regards to either music or voice control providers.

I hope that is the case. Integrating hardware with Alexa suggests otherwise though.

I think this is all about timelines.
Alexa was first out the starting blocks, sonos was loosing sales and needed to integrate fast, need to hit xmas 2017 sales, so rush out the sonos one and v8 beta controller.
From what I can see this has worked, with new customers buying sonos one because it has Alexa. This could be the life line sonos needed to carry on development in 2018.
For me I couldn't resist the black Friday google home £78 deal.

Makes sense, although I was planning on adding to my Sonos system but have decided to hold off to see where this is heading. I only ordered the Dot because of the cheap deal through Sonos. Frankly, it was a waste of £25.

FYI this is exactly the same as a Google Music Subscriber. I pay £9.99 / month and for that can stream via SONOS controller and have different songs to different rooms. All good - generally I like Google quality and range of tracks etc.

However, say I'm working from home and start streaming Google through the PC speakers (i.e. nothing to do with SONOS) - the SONOS will stop and the user gets something to the effect "already streaming in another room". Annoyingly it tend to be the first user who gets kicked out, but hey...

It's also a family plan to resolve this (14.99 instead of the 9.99), but I think that "associates" different google user accounts to one music subscription. In other words I'm 90% sure i'd have to run that PC stream using an additional account to the one I've setup the SONOS as.

Not great in my use case, but I can see why they're protecting their revenue... Music services as geared to mobile devices/usage, so if they didn't do this a whole household (and potentially other households "sharing account details" - obvs a bad idea for many reasons) would get the service for one "single user" charge.