Note that technically it is "fare class", not "class of service" (which refers to cabin booked) that is used. No, not all sites will show the the fare class, but sometimes it just takes a little hunting around. aa.com will show fare class on fares if you click "Details" link for a flight where it will show fare class under "Booking code". If you can replicate the fares on ITA Matrix, it will also show fare classes on flights.