Most of food is imported anyway, Switzerland is a very small country. This is a very silly argument, I'm sorry, it does not make any sense. "making shopping more complicated" what does that even mean.
What about pensions? We are talking about foreigners working and paying taxes in Switzerland, a lot of them in very specialized jobs. Health care? A lot of doctors and nurses are foreigners, too. But apart from all these cliches about how good immigrants are for the economy, the main issue is that all bilateral agreements with the EU depend on the free movement of people between Switzerland and the EU. Without that, Switzerland losses access to the EU market and becomes and isolated country. It is nonsense.