Sometimes they literally don’t have the ability to press 1.
Which is why I'm saying it should go through automatically after a short delay.
It's easy to say "just over staff" until you're faced with the reality that maybe once every five years, for a grand total of one hour, you're faced with call pressure 1000 times higher than the second highest spike. It's not viable to staff a response center to deal with thousands of people calling in the same bomb attack or shooting within minutes, when you normally see on the order of hundreds of calls per week.
What you need is the capacity to deal with 99.99... % of situations, and a safety mechanism to prevent the remaining situations from overloading your system more than necessary.
In a mass casualty event, you need to be able to filter out the people making redundant reports in order to effectively handle the important reports. You need to do that without blocking out the important reports, that's the hard part.

You do realist that "I am innocent, armed and will shoot if you try to arrest me" is possibly the worst conceivable way to avoid being unlawfully arrested, right?
There is quite literally nothing you could do to make it more certain that you will be either killed or arrested than trying to shoot your way out of being wrongly arrested.
I hope you also realise that the US has the highest incarceration rate in the world, and has a long and proud history of arresting and/or executing the wrong people. Literally any other system than the one you're advocating for is provably superior when it comes to preventing the wrong people from being arrested.