You don't get a jury trial with an infraction because infractions are punished only by fines. The jury trial comes into play only if your personal liberty is at risk, i.e., if your offense is punished by jail or state prison.
You are not entitled to a jury trial or appointed counsel in an infraction case because it does not carry the possibility of imprisonment. See Penal Code 19.6.
California law provides far more protection than the United States Constitution requires. In Federal courts, you don't get a jury trial or a court-appointed attorney in cases where the maximum punishment is less than six months.