Basically, their problem is that it's impossible to compete with Amazon on delivering a managed SaaS, and most of their money was coming from that.
In terms of the software itself and user freedoms, the licenses used have achieved their goals - ES is free, people using it can control exactly what they are running, can patch it and redistribute etc. No one owns ES itself, so it is Free Software in your sense.
The people who are having a problem though are the project behind most of the work on this. Now, whether this is a real problem (the company is struggling to remain profitable because of Amazon) or just a fake problem (the company is profitable but it's not growing as expected in some 5 year plan) I don't know, but this is the reason for this type of change.
Amazon has a small team for developing their version and at the end of the day, it has to fit into the operating constraints that they have. There are plenty of huge gaps in managed ES that the vendor can (and does) exploit.
It's an interesting idea to think that "Free Software" creates a sort of "distributed code base". In the sense that "code will be eventually pushed to the main repo when the patch is created". That's an interesting perspective.
Now AGPL might have, if it was used from the start... not because it would prevent any monitization, but because it might bring enough legal uncertainty for AWS to even consider using it
Open Source is for getting popular, and all of the arguments that Open Source people make against Free Software are about the ability to get popular (corporate usage and corporate contributors.) The reason companies use Open Source is because when you license something that way, it's theirs now. They're investing in their own property.
Free Software doesn't intend to have this problem, and if it sees a problem, it fixes the bug. You don't own Free Software, you own the devices that you install it on. You still might end up competing with someone, but you'll never fall behind.