The person you've constructed in this scenario is both blind and deaf. Such an unattended person is in extreme danger on streets with automobile traffic no matter what the crosswalk button does.
I agree that not all disabilities can be accounted for. However the more we account for the better - where accounting is all aspects of getting around. I don't know how to make it safe for a blind and deaf person to navigate streets safely - but I wish it was possible and as soon as I learn of something that works I'll support it.
At some point, a disability requires assistance. That is less true these days than in the past but still a last option.
It’s a simple button that clicks, and under the panel there’s a small knob that rotates. Click the button, then place your fingers on the knob and wait for it to start spinning. I can’t tell you if the crossing call button is completely broken (although you’ll figure that out if wait long enough), but broken call buttons in the UK are pretty rare, I’ve only encountered a small handful of broken buttons over 20 years.
I am most used to these ones specifically: https://c8.alamy.com/comp/ECW0FA/pedestrian-crossing-traffic...
Can be activated with your elbow, the thing beeps and the bottom lights up when you activate it.
In any case the buttons often vibrate specifically so that deaf people can feel it.