It strongly depends in nationality, and in this last year they have made rules more strict. If you are European and have good skill-sets, you are welcome. But if you are not European, you have to be special enough such for the company hiring you to be able to justify that there is no-one else in the EU that can do the job you are applying to.

This is not "just in paper". Some weeks ago I got a job offer widrawn from a company in Zürich because of this reason; me being a PhD in Applied Mathematics (granted by the ETH Zürich) but with a non-EU nationality.

They need better lawyers.

Alternatively, have you considered just getting an O-1?

They told me that they consulted with two "inmigration agencies" (I did not even knew that there existed such a thing), I would guess that they are experts in these issues.

My main weak point of entry is that I was applying to a consulting job in Data Science, and as such, it is not really possible to argue that there is no-one else left in the EU to take the job. Having a degree from the ETH indeed helps, but it wasn't enough.

They have enforced quotas per canton, which means that once filled, no-one else is getting in. Furthermore, Swiss bureacracy is the most strict one I have seen in my life, so there is no much wiggle room to bend the rules.

Either way, we can agree it isn't just based on qualifications and contribution to society as initially claimed.