I will say 20 is a lot but it is not uncommom to have a lot of different cheese.

First swiss often do fondue with 2 different cheeses, the usual moitié-moitié mix of Vacherin fribourgeois and Gruyère. Then sometimes you have 2 to 3 different raclette cheeses because you like different tastes. Then there are the cheese you might grate on your pastas (in my case I would usually use italian cheeses) and the different cheese you want to offer at the table in regular diners + the ones dedicated for the aperitives like Tête de Moine...It can add up quickly without being a nerd.