(I am a Foreign Resident living in Zurich for more than 10 years)
That's more progressive than Switzerland (but it varies by canton). No Swiss passport? No vote for you.
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.
Alternatively, have you considered just getting an O-1?
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.
Isn't Switzerland famously difficult to immigrate to?