Chazzans are fools

Apparently there was some kind of rabbinic stereotype that chazzans were idiots. I found two jokes relating to that:

1: It was once asked to a sage as to why it is that the chazzan makes kiddush in shul Friday night, but does not make havdala Saturday night? He answered: Have you not seen the Jerusalem Talmud "אם אין דיעה הבדלה מנין"

[That line happens to be the opinion in the Talmud that says "ata chonen" should be said on Shobbos]

2: It was once asked to a sage as to why everyone says that Chazzans are idiots? He answered: We know that if a chazzan makes a mistake, it is a bad sign for the congregants. And we also know that the rule is that if someone sends a shoteh for a sinful act, the sender is at fault. We see that a chazzan has a chazaka of an idiot.