No FOSS license would have protected ES from the problem they have with Amazon. Amazon is in full compliance with the AGPL for example, so if ES had changed the license from Apache to AGPL, nothing would have changed - that is why they had to move to a non-free license instead.
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.
As someone who has used OSS Elasticsearch, the Amazon managed offering, and the licensed and supported product, I don’t think that’s true.
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.
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.