They are in a position of having no seas and only EU on every side, which means things are getting more bureaucratic the more EU-Swiss relationship sours. Think border checks on the ground and flight restrictions in the air and the less than 10M rich people in the mountains can now trade only among themselves.
Swiss can have their policy, who said they can't have it? It's just that they can't make EU have the Swiss policy. If Switzerland wants to be a 3rd party country, they can do that and negotiate visa regime, import/export controls etc with EU like everyone else who is not part of EU or don't have a deal. They can be like UK or Turkey for example, or be have entirely different relationship.
It’s up to the Swiss to decide regardless, if population limit is more important than being integrated into Europe they can do that. What they can’t do is to have equal access to the single market like the other EU countries without the obligation that other countries have.