In many cases Non-L lenses are sharper than L lenses.
Most L lenses afford good optical quality but that isn't why they are L lenses. They are L lenses because they have been designed to survive the use of professional photographers like journalists.
If the L designation was about optical quality then lenses like the 17-55mm /f2.8 IS would be an L lens.
EDIT:
The L designation is a just a shortened form of the 'AL' designation used on earlier FD mount lenses that used aspherical elements which were expensive back then. apsherical elements are now much cheaper so even kit lenses can use them. The AL designation was then changed with the EF mount to market the preium lenses with superior build quality. L glass is normally good optically because it is aimed at pros, and the previous AL designation indicated the potentially superior optical quality with apsherical elements but tat requirement was dropped for the L series. There are plenty of L lenses without ASPH elements. Lenses like the 17-40, 28-300, 50mm f/1.2, 24mm TS are all renowned for not being the best optically but are L lenses. Lenses like 17-55, 10-22mm, 85mm f/1.8, 105mm f/2.8 MACRO (non-L), 65mm MP-E would easily be L glass in terms of optical quality but aren't marketed as such. The TS are really a great example - the 24mm TS is an L lens but has the worst optical quality of all canon TS, the 45mm and 90mm are much better optically but are not L lenses. The 70-300mm L is another good example, it is an L lens due the build quality (focus is also likely a factor here)