Airlines absolutely do file cheap fares that are only good some days of the week, and those days are often T/W or T/W/Sa. You'll sometimes see fares that are good M-Th also. (The old thing about buying airfare on Tuesdays, on the other hand, thanks to airlines matching sale prices that come out on Monday, is a good 10 years out of date).

And that's even discounting the possibility that airlines can (and do) restrict discount availability on high demand days. This has been easy to see all summer -- due to all of the leisure travel, in the markets I was looking at, Friday and Sunday were the two most expensive days to fly domestically this summer, and it wasn't even close.