Sadly it's often the most effective way. Companies pay a lot for social media monitoring and anything that gets a lot of tweets they'll act on.
Well obviously some companies disagree.
Interactions on Twitter are shallow, which makes support interactions risky and unsatisfactory for the customer ;-)
Which is why any sane company will only reply "Please mail us at ...".
Yes, we don't reply on Twitter since it became difficult to operate across multiple channels as we scaled.
I've just updated our Twitter bio to make it clear where to go for support:
"...at [email protected]", usually.
Is that really how you expect to get support?