Diesels are not good for taxis unless they are doing long distances. Most taxis are used in towns and for short distances. Their engines might not be subjected to cold starts as the drivers often keep the engine idling to provide heating but I suspect, having walked past plenty of these vehicles, that the noxious emissions are disproportionately high when this is done. Some urban local authorities are now actively discouraging diesel taxis while others are muttering about changes but don't want to upset the taxi drivers.
I guess you are right. 20-30 years ago diesel were taxis very common. With my argument I thought about the engine always being warm because a diesel needs a lot of time to warm up. Driving short distances with the engine not getting warm at warm is even worse, for the engine itself and the environment.
Nowadays, >90% of all taxis in Switzerland are hybrids and most of them are Toyotas, best quality out money can buy. Not so sure about Germany as German people have to drive a local brand like Mercedes.