It seems that Wrath has a peculiarly specific ability to work alchemy, which is that he can transmute something + his own body into a new modified part of his own body -- eg, becoming entangled in the bed at Izumi's house, and I think there's a couple examples in subsequent episodes of him giving himself a stone or otherwise modified arm to fight with?

Wrath doesn't seem to be able to transmute things other than his own body into other things not his body, the way Ed and Al often do (examples other than Ed making a blade of his automail arm). I'm guessing that's why he can't do the particular kind of alchemy required for the Philospher's Stone.