In particular the Black Plots for Stage II (Saruman and Denethor) requires high amount of influence in the SP (5 and 8 respectively). Further, the Plot Step comes before Sauron's Action steps, so denying him enough influence in the SP means one more turn when he can't play that Plot and in fact has to spend an Action to increase his SP again. Denethor Plot in particular is vulnerable, since Sauron's SP during Stage II is maxed at 8, so any reduction will nerf that Plot for another turn. Only other Plot that I've seen denied through reduction of the SP is the 4-influence requiring Yellow Plot at Barad-Dur, though only in Stage I. But Sauron in general wants to have three Plots at all times or if he doesn't, play a new Plot, preventing him from playing a Plot means another turn when a Sauron token doesn't move on the Story Track.
Another, less common use is the denial of certain Shadow Cards, but this is less effective since he can re-play the influence and then play the card, should it have a timing of Sauron's Action Step. Mostly I'd say, Shadow Pool reduction is key during Stage II, keep him either below 5 or not allow him to have 8 (which is also required for some of the better Shadow Cards). When playing Sauron, Thranduil is the one character I least want to see out there. Luckily, I think he is actually the rarest one. As for Wisdom, I've found that Wisdom 2 is okay, Wisdom 3 is about the max you'll ever need, for Sauron pumping up locations to 4 influence to make them perilous is just too expensive. So only Thalin really needs +2 Wisdom (but he needs +Wisdom BAD), for others, depending on the board situation, I'd be much more likely to look at reducing the Shadow Pool than picking up +1 Wisdom. Even getting chains of 3 influence isn't that easy or cheap and worse, they can still be cut down to one unless you have stretched your influence chains to two Shadow Strongholds (which I'll grant you is easy for the Anduin/Mirkwood locales).