Can't get cy.intercept to add custom headers

[mzedeler]

I am using Cypress 6.4, and like the documentation states, I am trying to add headers to all outgoing requests (in this case, to switch off caching), and it doesn't work. Before any other calls to cy.intecept, I do this:

      cy.intercept(/.*/, req => {
        req.headers['cache-control'] = 'no-cache'
        delete req.headers['if-none-match']
      })

If I look in the network tab, the requests are not modified. Also, I can see that the request rewriting block above is actually called on every outgoing request.