Price discrimination allows producers to capture consumer surplus from consumers with a greater WTP than the otherwise price, and to offer the product at a lower price to those with a lower WTP.

In a monopoly, this means that the quantity supplied may be greater, but it would still be no greater than under perfect competition (necessarily so since the monopolist would never offer the product at a lower price than their MC, which is where price would be under PC). You can see this because there is no consumer that would buy under price discrimination that wouldn't buy under PC, and everyone with a WTP greater than MC buys either way.

Anyway, I agree that price discrimination results in the producer capturing more consumer surplus, but it can potentially be beneficial for those with a lower WTP in return for hurting those with a higher WTP.