That is standard procedure for one simple reason. It saves lives!
There are many more firefighter/EMTs units than EMS crews. Every department I am familiar with (and having been a volunteer firefighter for over 30 years, and have a grandson that is a Firefighter/Paramedic it's a few) the minimum requirement to be hired is firefighter certifications, and EMT certification (or higher).
Statistics clearly show that trained medical response sooner saves lives.
In my area, there are about 20+ EMS units staffed with Paramedics. At any time, many of those are busy taking care of patients or at the hospital transferring a patient to the hospital staff.
Conversely, there are probably 80–90+ firefighter/EMT crews that are within a closer distance to a person having a medical emergency, and can begin life-saving care minutes early.
But if you still view it as "the god damnedest thing" then tell the 911 dispatcher not to send the fire department when your loved one is having a heart attack, not breathing, or bleeding out...