Does everyone in Switzerland know the name of their president? Does anyone care much who it is? Does the selection of a particular individual to the presidency matter fundamentally to Switzerland's prosperity and stability?
The short answer to these questions is "No". Switzerland's president is indeed the head of state, but the constitutional arrangements are such that he or she can never have a significant amount of personal political power. The president is not chosen by the electorate at large and cannot pretend to be "a champion of the people". Instead, the bicameral, democratically-elected Federal Assembly decides at four-year intervals the membership of the seven-strong Federal Council. From this seven, it picks a new president every year.
The constant rotation of the head of state and the subordination of the Federal Council (the executive) to the Federal Assembly (the legislature) ensure that power is never concentrated in the hands of one politician or a clique of politicians. In this sense, Switzerland never has "political leaders".
Does everyone in Britain know the name of the prime minister? Does anyone care who it is? Does the selection of a particular individual to the premiership matter much to Britain's prosperity and stability?
From the early hours of May 7 to the afternoon of May 11, Britain did not have a PM in the usually understood sense. Gordon Prime still resided at 10 Downing Street, but he had lost the general election and was not a meaningful and effective head of government. Sure enough, David Cameron, Nick Clegg and their colleagues, were engaged in detailed negotiations about a wide political agenda. Nevertheless, for a few days Britain did not have a "leadership" able to take executive decisions. For those few days, the UK was in a constitutional position similar to Switzerland's.
To judge from many of the headlines in the newspapers, the absence of a government, a definite new prime minister and an identifiable political leadership was a calamity. Perhaps the sky wouldn't fall in, but pundits complained as if the country were like a company ("UK plc") without a chief executive, a ship without a captain or a school without a headmaster. Since companies without chief executives, ships without captains and schools without headmasters are notoriously inefficient, the implication was that Britain's operational capacity was somehow at risk. Enormous relief greeted the announcement that Cameron and Clegg had reached the basis for a coalition deal.