I'm sorry, but I really don't understand why this is so hard to grasp. You might as well ask why the world isn't shut down for three to four weeks, to stamp out the virus (almost) completely. The answer is that the real world doesn't work in a binary fashion, it's not 0% or 100%, governments have to try and find a balance between letting life (or rather their economy) go on with as little impact as possible and managing virus spread. As such football clubs are allowed to keep playing, given they adhere to a certain safety protocol that's been negotiated with the politicians.
As such health authorities in Leipzig have the position that they can manage and supervise the risk of Leipzig's team, but they drew a line at granting an exception to invite the whole Liverpool squad, Liverpool staff, UEFA officials, British journalists, British broadcasters and god knows who else into their city. The Leipzig team is something they have a working relationship with, who they build up some trust with, all those other people that would've come for the Liverpool fixture are not. Therefore it would have meant significantly more risk and significantly more public health resources required.
Also:
The "British mutation" already spread to Europe, this is about curbing further spread.
Public health officials of the city of Leipzig, to my knowledge, still can't confiscate passports.