The Europeans seem to have better luck. There's Edelweiss of Swiss and Eurowings (and Condor?) of LH.
WK and LX don't overlap routes; WK handles the more leisurely routes and LX handles the high J routes
A333s: WK is J27-Y+56-Y232 for 315 seats; LX is F8-J45-Y183 for just 236 seats
A343s: WK is J22-Y+76-Y211 for 309 seats; LX is F8-J47-Y164 for just 219 seats.
(LX B77Ws have the same seat dimensions and seat products as the A333s in F, J, and Y, just with different seat counts.)
LH Group keeps LX and WK with distinct products and seat dimensions...similar to how Eurowings (LH Cityline) and LH Mainline wide-body A343s and A333s are distinct; EW/Cityline is low J while LH Mainline is higher J (the A343s and A333s at EW are 300-seat planes with a very small BIZclass, while Lufthansa J is much larger).
LH and DE (before DE was acquired by Thomas Cook) also had distinct products and didn't ply the same routes. While LEVEL (out of Spain) is on the IB AOC (for now), it is distinct as being out of BCN rather than MAD.
That said, within Europe, what really distinguishes legacy from LCC in terms of short-haul, aside from a few outliers like AY?
As for why you don't really see it in the USA...there is a desire in the USA to maintain a premium economy or first class on full-service or major regional airlines. It would take dropping domestic F, in my opinion, by all of the legacies.