This franchise is dead, and rightfully so.
At this point, I think you're letting your personal (and very legit) dislike for F13 overshadow common sense.
The franchise is NOT dead. If it were, we'd have no Jason X to argue about! What I think you mean is that you WANT the franchise to be dead. While I respect your opinion, opinions are not fact.
Regarding the "other" franchises, you claim that they're "all dead or will be dead". Hmph. That covers a lot of ground. Star Wars still has two movies left to go, plus all the nonstop tinkinering Lucas will do once the new trilogy is complete. That series may not be "dead" until long after Lucas is.
Indiana Jones? They've been discussing this one for years, and it probably WILL happen. Why? Well, for the same reason Jason X is being made: Studios want to MAKE MONEY, and a "known commodity" is nearly a sure thing at the box office.
LOTR? Still two movies left to go, and then I GUARANTEE someone will come along (maybe P. Jackson, maybe someone else) and direct The Hobbit or The Silmarillion for New Line. Why? Because there's boatloads of CASH to be made.
When the studio execs gather around and decide which movies they're going to start production on, and someone mentions a Part 4 or Part 8, the reaction is NOT going to be "Sheesh, that again???" The reaction will be "How profitable will it be??" You think the F13 series should die out now. That's your opinion, and several million people probably agree with you.
But the bottom line is simply this:
No series will truly DIE until the films become unprofitable.
You're up, T!