The antes are also P/2 units, so you would have to write them as PU/2, and then the pot would be PU.
Hopefully now you see why that's not quite right.
In general when studying fixed-limit games, we set the pot to be a variable (in this case P) and the bet size to be 1.
When we're studying big-bet games like NLHE or PLO, we set the pot to be 1 and the bet size to be a variable (usually B or s).
I hope that's helpful.