Partially my bad; I should have summarized it a little.
Ours in the hallway outside the kitchen sometimes goes off if we are broiling. We never use a silence button or a ladder. Just get a newspaper, fan it under the detector, and the density of particles will go down enough to turn it off. Then we close the pocket door between the kitchen and the hall to prevent a recurrence.
Our ceilings are low enough - and I’m tall enough - so that I can reach the button without using a ladder, though I need one to change the batteries. The detectors in the bedrooms and offices are over the door - close to the ceiling and close to where smoke would get in.
I wave my newspaper to turn off mine, which costs considerably less than $129. 
The OP posed a good question. I have often wondered that.
You replied with a good answer. I was happy to have read your answer and feel that I learned something useful there.
Guess there is a reason for it to be high up, ignorance fought!
Still, they should redesign the thing. Ideally, the smoke detector should have a big button to turn it off, like an Apple mouse whose one button is practically the whole face of the mouse. Or maybe it needs to have a little hanging string so you can pull it like a curtain
A smoke detector with an off switch will turn out to be a smoke detector that is turned off. Not very useful that way.
I have never, ever seen a smoke detector that didn’t have a button to silence the alarm.
There’s two in this house - one right outside my bedroom that has two buttons, one to test the alarm, one to silence it (labeled Test and Hush, respectively), and one on the stairs into the basement, where you push and hold the cover to do both. Every smoke alarm in every house I’ve ever lived in has been the same way.
And this is why they tell you to crouch or crawl as you exit a smoke-filled building, as you have a better chance of breathing down there.
For those annoyed with false alarms from cooking, get a smoke alarm specifically aimed at kitchen/bathroom/etc areas, a photoelectric only one. I got a First Alert model SA720CN (including an escape light - yes, and a silence button) after the previous one even went off after a too-steamy shower.
Can’t you hit the button with a broomstick? Put a tack on it if it’s recessed? Actually, if it’s recessed, you could tape a pellet over it so it becomes protruding.
In a kitchen area a heat detector should be used.
This was a prep room where they had installed a convection oven because there was no room left in the kitchen. I’m sure they were also using the least costly method of satisfying regulations. If the oven had been properly vented it wouldn’t have been a problem, but that would have cost a little more.
Lithium batteries are what I use in my smoke detectors. They last some 10 years under minimal load like what smoke detectors draw.
All the smoke detector issues here are solved by getting the nicer detectors of the appropriate type for the room, and putting them on house wiring. They do not go off from your shower, you need to make a pretty terrible mess of dinner to set them off, and if you do you can push the button on one of them that is at a reasonable height and they will all stop beeping while you clear the air.
Worth the investment, and you can hook any carbon monoxide detectors in as well.