Land area is a non-issue. Google says Switzerland produces "80 to 90 million tonnes" of garbage per year. Assuming that garbage has the same density of water, and a landfill is 10 meters deep, a 1 sq mi landfill will last 287 years. Moreover, Wikipedia says Switzerland has 15,940 square miles of land, so that will only take up 0.006% of the country's land area.
>eventually will leak lovely chemicals into groundwater
this is a non-issue in modern landfills because they're designed with various mechanisms to prevent that from happening (eg. lining).