Then what good does it do? They won't change their mind, and you know you've made an irrational argument, so where's the satisfaction?
This was already addressed. The process of changing minds is not a 1-step process. It does not occur merely because you point out the logical flaws of an argument either. To get someone to change their beliefs, they need to become uncomfortable with their existing beliefs and/or become convinced that some other beliefs are in their own best interest and are more drawn to those.
Pointing out that their own views or behaviors are hypocritical will not change their beliefs from X to ~X, but it at least reveals that there is at least some defect in their views. They cannot continue on as is. Whenever they launch some dumb criticism that actually is more dangerous to themselves than it is against the intended target, they will show some more restraint about using that dumb criticism. They will rethink that more. Again, it will not be immediate. It probably would not be a complete reversal. It is not the entirety of the exchange. But some degree of change is more plausible. It is just one part of the overall process, not the entirety of it. As soon as they cool off with the childish trolling rhetoric that backfires against themselves, then there will be some room for a more mature conversation to grow.