It's been 12 years now, since 1995, that the Road World Championship is won by one-day race specialists. 
Although from 1980 till 1995, 10 times out of 15 the tital was won by riders with a Grand Tour victory in their palmares: Hinault, Saronni, Zoetemelk, Roche, Lemond (twice), Bugno (twice), Armstrong, Olano.

Is it because the racing calendar pushes the event at the end of the season, of the not-so-selective courses, of an exasperated racing specialization?

Undoubtedly having a World Championship (WC) that happens at the end of September of at the beginning of October means having the majority of big stage races specialists with little energy and motivation: the best riders usually sign the contract for next year right after the Giro or the Tour.
I believe that bringing back the WC in the month of August could be a good solution in order to find the Grand Tours champions motivated for victory. 

The courses of the last few years certainly did not favor those athletes who excel at climbing and/or time trialing, that is those cyclists who have a high Anaerobic Threshold (AT), able to maintain good intensities (350-450 watts) for a long time.
The circuits of recent editions proposed short hills, 1-2 km long, taken at a very high speed from the flat sections, therefore reducing the intense effort to 2-4' only. 

As a consequence, this was ideal for powerful and fast riders able to express high power outputs (550-750 watts) for a few dozens of seconds, with a good endurance base too.

Stage races' cyclists are excellent endurance athletes, but they are not so at ease when compelled to produce several times such wattages required to counter the attacks and accelerations of one-day races specialists.
Probably, compared to the last ones, they also inferior recovering and recycling skills (see articles) of the lactic acid produced during the high intensity effort.  
Moreover, specific training such as the kind done to improve AT, essential for long climbs typical of stage races, does reduce lactacid power and capacity, just as anaerobic specific workouts done by one-day race specialists, do tend to lower AT.

Proposing climbs that are 8-12' long in the next circuits of the WC surely would see stage race specialists more competive.