In the same way the AGPL satisfies it, you can run it for any purpose if you provide the source code to users.

Well, the linked page indicated that copyleft is something that applies only to distribution and not use, but I guess the AGPL shows that that's not true.

Nonetheless I don't agree with the GNU's claim that copyleft doesn't reduce freedoms. Of course a permissive license provides more freedoms: it's right there in the name

But this issue isn't really about permissive vs copyleft licensing anyway: Had Apache used a copyleft license with Lucene, Elasticsearch would have never existed.

But Amazon is hardly offering Lucene as a SaaS offering, don't they?

If they did, should that mean Elasticsearch can't?

I don't see the point there.

Lucene is a library, you can hardly offer it as SaaS. It's gluework.

On the other hand, Elastic is much more enduser software, which is much more routinely abused for SaaS hosting by larger corporations.