Why is it that professional lawn scarifiers don't have these moss removal tools?:
The Stihl you linked to claims to remove moss; it appears to have 6 settings to raise or lower the scarification, so it's possible that one or two of those settings is better at removing moss, but this is a question for the manufacturer really. The AL-KO does not mention moss removal, and again, whether it's intended to remove moss or not is a question for the manufacturer.
In my experience, mechanical scarifiers do scrape off moss as well, provided the lawn has been cut beforehand.
I decided to contact AL-KO and they told me, that the moss removal tool is for lite removal that is not ment to even touch the ground and hence the weed roots are not removed.
Scarification is the prober way and professionals only do that.
As a side note, they mentioned the cut level should always be at number 1 or 2. It is only set higher (deeper) when the blades are worn down.