It matters more than most owners expect. Clients tolerate a problem taking a while to fix far better than they tolerate silence, and this is the number that decides whether the wait feels handled or ignored. It is also the metric most within your control, which is why it belongs in an SLA where resolution time often does not.
The common cheat is counting an automated acknowledgement as the first response. The ticketing system replying instantly makes the metric look excellent and changes nothing about the client's experience — they know the difference between a receipt and a person.