Well maybe you shouldn't be so amazed. There is a perfectly rational explanation in this thread from someone who actually does this for a living and has stated it is preferable the pax are taken off first. Be elated, you have been educated and your sense of being "amazed" is misplaced
I am absolutely sure the EMT who posted would prefer not to have to swim upstream against a line of passengers with their luggage all the way from the entry to the jetway and especially the 30" aisle of a narrow body.
If Emergency Service informs the crew that they'll be there in 30 minutes, sure, disembark the passengers. But it takes 15-20 minutes to empty a plane - it's another common complaint around here, with plenty of people arguing that anyone who stands up when the bell rings is a Type1 jerk
"what's your big rush DYKWIA?" - and it's rather more likely EMT will get to the gate as disembarkation is in process. That's a disaster, and someone somewhere will die if that happens.
Sorry if your life is being delayed by a few minutes, even a couple of hours if you miss your cxn.