Oh my God. Air France using widebodies on shorthaul routes. I just imagine this forum with questions like "Will my upcoming Paris-Lannion flight have NEV3 or NEV4?"
Nah, just kidding.
brunos, I can see you logic and obviously we see other markets in the world where it happens. But we can also observe how it happens less and less in the US and Europe these days. BA used their 767 on many European routes: Paris, Stockholm, Frankfurt, Madrid, Rome, Dusseldorf, Munich, Milan, etc. But they had a dedicated sub-fleet of B767s. The old Swissair scheduled MD-11s to London and Munich every morning, with the First Class seats given to Travelclub highest tier members. Similar on the Malaga flights in summer. And of course you had the times when the likes of Air France, Lufthansa, KLM, Swiss, Iberia all had fleets of A310 and A300s that were used on European and domestic routes.
I can remember AF using some of its ORY-based B747-400s to Ajaccio in summer.
But all of that was in the past.
Today, Iberia uses A340s or A330s on some of its Madrid-Heathrow flights on a regular scheduled basis. That is the only one I can think of. Also in the US widebody services are limited to hub-to-hub routes where one of many rotations sees a widebody plane and to the LAX/SFO-JFK market, plus the Hawaii routes (but are they "shorthaul"?). Gone are the times where DC-10s flew to places like Milwaukee, Buffalo, Oakland, etc.
There is one other consideration on top of all the reasons already given here: longhaul planes don't like taking off and landing too frequently. Their frame and structure especially around the gears are designed for a few long cycles. For instance, the B747-400D (where "D" stands for "domestic") that was ordered and used only by JAL and ANA for their high volume routes in Japan had a reinforced landing gear. It also didn't have winglets, because winglets don't make that much of a difference on shorter flights.
Would I like to be in a proper business class seat even on short flights? Sure! But I guess that could even be achieved without using longhaul planes.
Would it make sense for airlines to have dedicated widebody fleets for European routes? My impression would be that most routes are too variable in demand. There are days when you could fill a widebody plane and then airlines sometimes just sub them. But other than that it is easier to react to changing demand patterns by varying between A321/A320/A319/A318 and maybe taking out a flight or two.