Thirst really is trashy in any deck but Slaver (sorry, Brassman). In a deck that can't take advantage of the graveyard, you either pay 3 mana for +1 card advantage or 3 mana for +2 card advantage and loss of valuable mana (whose buildup is the whole point of a control deck in the first place). Say what you will, but it might be interesting to try out a mix of Ophidian+Deep Analysis. Ophidian is good for reasons already discussed, and Deep Analysis is definitely one of the best card-draw spells in the format, and can be used easily with Mana Drain.
The reason I don't play Ophidian is because here in the Netherlands storm combo is extremely popular, and it takes 4 turns to see the same amount of cards with a Phid than with a TfK. Though obviously better in the late game, going against storm the impact TfK has on the game immediately I think beats the long-term effect of an Ophidian. Also, since these decks are unpowered, you rarely ever end up discarding mana, the only time I ever discard lands is if I have enough or I have a crucible out. Also, TfK functions as a means to get DSC back in the library, without having to rely too much on a BS + fetch.
As for Deep analysis, the fact that it's a sorcery really hurts, since you don't want to tap out on your own turn. Meaning you'll only be able to play it after draining something. Also, you don't really have any other way than playing it to get it in your graveyard, so you'd be spending 6 mana an 3 life for +3 card advantage on your own turn. Also, the first time you play DA, it is strictly worse than TfK. All of that and the fact that is is a big drain target for me in enough reason to not include it. If I had to cut TfK's I would rather go for intuition/ak, which I've chosen not to play because it uses more slots and is more mana-hungry.
@ Kelme
I will try and play with B2B, since there were some good points about B2B having impact immediately, but CoW should not be underrated. It functions great with a fetch-land to thin you deck and doubles as a lock with a waste/strip. The only problem I think is that it is quite a bit slower than B2B, so I think I'll test it and see which one I like best.