I can use a proper touchscreen phone just fine, as its OS is advanced enough to run a screen reader, and its touch screen can precisely locate where it was touched and supports flicks, swipes and multi-finger gestures.

Proper touch screens have some very important advantages, notably being able to show different controls at different times. You want to have a different button layout when you're typing a text than when you're watching a movie or playing a game. Physical buttons make this impossible.

Even blind people benefit from this, modern phones have a mode where you can use a touch screen to input characters in Braille, treating different parts of the screen as keys on a brailler (think piano with 6 keys). Each combination of these keys, pressed or touched at once, inputs a specific character[1].

Now touch controls, like those you can find on a washing machine / coffee maker, make no sense. There's no screen behind them, so they're not dynamic in any way, and the primitive software of such devices (as well as the need to seell them in multiple countries without providing specific support for any particular human language) make accessibility impossible to achieve.