Yes, thanks to their vast operating profits from the cloud they have a P/E of ~3000.

Let's be generous and assume Amazon could push a button and run the rest of its business at break even, and that its revenues from the cloud are pure profit -- its P/E would only be somewhere between 50-70.

It depends whether you assume that virtually all servers will go to the cloud and Amazon will have monopoly market share in the cloud.

I think a business strategy that assumes "someday in the future we'll be a monopoly and charge rents" isn't a good one.

Good point. Overpriced products that people think they can't live without are great for profits.