I know that the comparable Portuguese system, the Pousadas, have been privatized (at least in terms of management) and are now run by the Pestana group. Maybe that's what will happen in Spain. I can't believe the system will shut down. What would they do with all those castles and monasteries?!
Footek, as far as paradors on Caminos, here are some of them, but I may have forgotten some
Frances -- Santo Domingo de la Calzada (2), Leon, Villafranca del Bierzo, and of course Santiago
Camino del Norte has a few -- Santillana (2), Villaba, Ribadeo
Invierno -- Monforte de Lemos
Via de la Plata -- Merida, Zamora, Zafra
Camino de Levante -- Albacete, Avila, Toledo
Sometimes there are very good deals on paradores. I stayed in the one in Zamora for two nights for 60 euros a night. So if you're looking for the luxury of ridiculously thick towels and the highest thread count sheets I've ever slept on, you could give it a try. The staff has never blinked an eye at me and my backpack, though as the NYT article says, the staff can be generally a bit stand-off-ish.
Of course not all pilgrims have the finances to consider a night in one of these places, and opinions are divided among others about whether it "feels good" to take one or a few nights in the lap of luxury, but I say chacun a son gout. (or at least I think that's how it's said). Buen camino, Laurie