Glad to hear it helps you Manfred,
The sensitivity of the input is the issue.
Remove R1 as it's likely irrelevant,, R2 is the dominant load.
Try looking at it this way.
As *mictester* noted the input Z is way too low to be useful for guitar.
OK you change R2 to 1Meg and you raise the input sensitivity,, BUT as R6 is already 1meg then you have a very sensitive input with high gain. ( a recipe for noise) Yes a much better interface for the PU's but now you have also made the input very noise prone.
The Hiz Buffer resolves this problem by giving you a sensitive HiZ input with NO Gain and a low Z output
Then the opamp input only needs to be low input Z and now you can crack the gain with far less noise.
Anyone can test this out on a breadboard to see/hear just how well this simple trick works.
I'm only an amateur hobby geek and hopeless at all the maths needed to explain intricate details but I've built enough land fill to learn that Noise is a huge problem for a lot of these hyped up dirt circuits.
There is some very good explanations and info on how to resolve noise problems in the book the Art of Electronics.
Even a high gain well designed basic 741 opamp dirt circuit would likely beat a crap design using the most Exotic opamps when testing noise issues.
As it's not the quality of Actives in a circuit it's how well you design the passives that run it.
Same goes for the gold plated dust on NOS valve gear.
It's not the Valve,, it's the design of the passives that make it work.
If more time was spent learning R/C maths than chasing the best opamp or Nos parts we would all learn so much more and spend a lot less money chasing our tails. Rant over
Others here are far more qualified to explain the maths for working out the complexities.,, heck I'm just a muso with a hot soldering iron who learned enough to build a few successful circuits.

Phil.