I find the American rule of having one representative per district flawed, as it gives an unfair advantage to large parties. In the Swiss system, I can cast 20

I find the American rule of having one representative per district flawed, as it gives an unfair advantage to large parties. In the Swiss system, I can cast 20 votes if my state has 20 representatives. This allows a party who get 5% of the votes to win a seat. Also, voters are free to vote across party lines as they like, but one can vote at most twice for the same candidate. That allows to influence the ranking of candidates within parties, which is for example not possible in Germany, where the voters can only choose between pre-arranged lists provided by the parties. The Swiss voting system allows for much more elaborate voting strategies than any other. I, for example, usually start with the list of my preferred party and then remove all lawyers and career politicians, because I think they are over-represented. I wonder why there aren't many countries that copy the Swiss system of electing the parliament. Maybe because it gives more power to the voters than typical politicians feel comfortable with?