If offering free support is too expensive, then they shouldn’t offer free support, instead of externalizing the costs by wasting the time of every customer who calls.
Charge callers some small fee and refund it if it was a real issue.
Paid B2C support is a real tough sale. A lot of low-cost airlines don't provide support at all (if not in person), I guess because it's not practical. If costs could be covered this way, everyone could offer support. Even Google! And yet they don't.