I think some do use regular wifi, especially the amazon ones, but with a button you have an advantage where you could just stay idle and off the network most of the time, and only connect to send an event when pressed.
That likely increases your latency by a fair bit. Most of my devices take a second-ish to connect, configure the WiFi stack and start sending data.
I’m not sure I’d want a full second of latency on button presses. I would have figured Amazon used BTLE to the Alexa and used it as a BT to WiFi gateway
BTLE and/or their IoT mesh network (Sidewalk?) would be a good way to go too, but if it's just a button to reorder laundry detergent or something then I don't think even a 30 second delay would be a deal killer for most people.
I’m not sure I’d want a full second of latency on button presses. I would have figured Amazon used BTLE to the Alexa and used it as a BT to WiFi gateway