First, a typical Mauser, (let's take this one for example, mfg 1937) was mfg over 70 years ago. We are capable of much better machining accuracy today.
Second, They were cranking these out as fast as possible as Germany started it's little trip across Europe.
Third, Other than the sniper versions, which probably received a little extra TLC and were also scoped, these were built for the infantry where 300 yard shots would be considered a very long shot, especially with just having iron sights.
If you really want to reach out to 800 yards, you really need everything to be right on. A thousandths off here or there could make the difference between a hit or miss.
None of the processes described above removed a lot of material, but they all removed some.
Starting with a receiver where you know everything is straight, square, true, flat, parallel etc. is step number one for the type of accuracy you are looking for.