Not everyone is capable of walking long distances, using bikes or electric scooters. Taxis are a form of public transport.
I'm not saying everyone who uses them needs to use them, but if you ban them outright you ban certain people outright, which is discrimination in the absence of alternatives.
Can't make this argument any longer. Plenty of electric vehicles which can serve as taxis, and in the UK they manufacture one especially for the purpose. [1]
Amsterdam in particular (mentioned in the GP) has excellent metro and tram networks, so you never have to walk far if you don't want to.
That said, the trams can still be really awkward if you're disabled, particularly if you're in a wheelchair as, somewhat incredibly in this day and age, not all trams are wheelchair friendly. And on those that are, you are reliant on the conductor to manually push out a ramp for you.
I do also agree that taxis are a form of public transport, and I don't personally think they should be excluded from places that buses and trams are permitted.
At least in the US, you could make a compromise along ADA lines.
Maybe I'm ignorant of this exact situation, but if it's only one road that's closed, shouldn't the other roads be close enough? What stops a car from entering an alley so someone with limited mobility can enter it?
I'm not saying everyone who uses them needs to use them, but if you ban them outright you ban certain people outright, which is discrimination in the absence of alternatives.