Reading DStahl's blog post on dilithium, I get the impression that Cryptic is trying to de-emphasize the STF missions, and get players to spend more time playing other (easier) endgame content.
I (and many other people) really enjoyed the STF missions. They were challenging, and with the gear I now have, most of the other endgame content is too easy.
In keeping with DStahl's idea that dilithium is designed to reward players for playing specific content, why not have a rotating dilithium bonus? So that based on a preset schedule (either hourly or daily, I'd advocate daily), one or more specific missions give a significant amount of dilithium. That way, players trying to optimize their dilithium gain will end up playing a wide assortment of missions (STFs, Terradome, SB24, Gorn Minefield, No Win Scenario, etc), and you'll be playing a different mission tomorrow than the one you played today, or yesterday. This could either supplement or replace the existing PvE dilithium rewards.
And to preempt those who will surely jump on me for advocating DStahl's unpopular dilithium plans, I'm not saying I agree with it, like it, or that it's what I would have done in his place, only that he's the boss and we are unlikely to change his mind about the basic function of dilithium.
If you want dilithium to reward specific content, at least make it not always be the same content, so we can get more variety without you having to program more missions.
TL/DR Version: Bring back the STF calendar, which gave bonuses, including dilithium bonuses, to specific missions on specific days, but expand it to all PvE content, not just STFs, and make every day a bonus day for something.
I could live without the dilithium rewards. But you are right that there must be motivation to do different stfs. Otherwise people just all do infected space all day. They must either give different rewards or force the player to do different stfs. I do not stand against the new system in general, but it cannot stay the way it is right now!