(My Klingon alt is also making steady progress - she has rank 4 Marauding for all the teleports, and is slowly completing chains despite roster limits - I have not paid to increase her roster size, and do not intend to.)
DOFF missions award dilithium ore, which is required for certain types of crafting and purchases and can be exchanged for Cryptic cash store points through a player exchange. As of now, my earnings have added up to around 1400 CP (plus 800 CP that I actually purchased). A portion of that balance went to unlocking the energy credit limit for my account (400 CP) and to increasing my main's duty roster to 200 (580 CP), leaving me with around 1200 CP in spending currency - $15 worth. This is more than half of the cost of the high level premium ships in the cash shop, though my income rate is dropping due to a steadily increasing exchange rate and diminished time in game.
That said, the scorecard I'm actually tracking right now is my energy credits. Now that I no longer need more officers for my crew, I'm selling stuff on the exchange for hundreds of thousands of energy credits daily. I don't really need energy credits for their own sake - I don't actually play any of the conventional game and therefore have little need for gear - but it would amuse me to pick up one of those unethical lottery box ships that people are wasting over $100 in real money on in exchange for in-game currency.
Of course, if I did this, I would be indirectly financing Cryptic/Perfect World's gambling activities. The person who paid money for keys to open lottery boxes only to put the ship on the exchange did so because the roughly 80 million energy credits were worth the real money to them. The players who buy my surplus duty officers are in turn providing me with the credits to convince that other player to buy lottery box keys. On one level, this is a good thing because it is a way for my presence in the game to contribute income even when I personally am not paying - good for the game economy. However, it also means that it's effectively impossible for anyone to boycott the lottery system unless they give up the entire in-game economy.
Not sure how I feel about this, and I guess I have a good while to find out - I am less than halfway to the energy credit balance I would need, and I don't even want the Ferengi ship that's currently on offer. It's definitely an interesting quirk to the system though - no wonder so many players feel so powerless to stop them.