They do now, but the problem is that a bank does not necessarily raise 11 months money in every major currency every business day. So you would end up with patchy submissions. Not sure what approach they now use for that. I presume they must do some form of interpolation.

The other thing is that Libor is an ancient instrument, created before capital markets had the size and liquidity they have today. The market must have been even patchier then.