"Lugers must have been an armorer's nightmares. If something broke, you couldn't just slap in a part from the bin; it had to be fit."
Well, that is what is often said. But I have many times "slapped in" parts in Lugers and never had to fit any. By the Luger era, tooling, especially in Germany, was plenty good enough that fitting parts was not really required.
As far as I can determine, the method of preliminary assembly and numbering parts for re-assembly after finishing was nothing more than a holdover from earlier times. It was done, not only for the P.08, but for the K.98k as well, and there is rarely a problem with "drop in" parts for the rifles.
The practice of inspecting, stamping and serial numbering each part must have been a huge drag on production, and there does not seem to have been any reason for it, except that military contracts called for it. And why did the military require it? The best answer I could ever get was simple "because we had always done it that way". To the military mind, that is a good enough reason.