Why a Swiss business would hold one
Switzerland gives you three quite different Swiss signals and they are not interchangeable. .ch is open to anyone anywhere and says nothing about the holder. .swiss is federally administered and says the holder has a demonstrable connection to Switzerland. .zuerich is narrower than both and says something neither can: this entity is on the commercial register of the Canton of Zurich, with an address in the canton, and the Canton itself allocated the name.
That narrowness is the argument. For a business whose market is the canton rather than the country, the extension does work in the address bar that a tagline would otherwise have to do, and the eligibility gate means it cannot be diluted by registrants with no local footprint. It is a complement, though, not a replacement. Customers reach for .ch by reflex, so the sensible pattern is to hold the .ch as the address people guess and put the .zuerich on the vehicle, the shopfront and the letterhead where the geographic claim is the point.
The Canton's policy is stricter than a typical registry's
The governing document is the Canton's Domain Name Registration and Use Policy, Policy No. 1, in its 6 February 2021 version. It sets a restricted registration model with both registrant and local-presence requirements, and it is unusually explicit about what happens afterwards: compliance must be maintained for the whole duration of the registration, names may not be licensed or made available to third parties who would not themselves qualify, and privacy or proxy services are prohibited outright.
The Canton also reserves the right to monitor use routinely and to investigate on its own initiative or on complaint, and to deny, cancel, transfer or lock a name where it finds a breach of the registration and use policy or the anti-abuse policy. Acceptable-use limits go beyond the usual abuse categories to include names or content that mislead about geographic origin or official status. As a reseller we submit the registration with your UID and cantonal address, manage renewals and the technical configuration, and tell you before you pay if we think an application will not clear.