It's best if Jason stays dead, since not only is bringing him back demeaning his sacrifice, but also, it's like a stab of guilt for all those people who used to hate Jason because he wasn't as good as Percy.
P.S :- I used to be one of those mindless idiots until I read the HOO with no bias and really loved Jason and was really furious with myself for hating him.
Also- sacrificing someone like Drew, Alderman, Gabe, Umbridge is severely demeaning his character.