Soren - I don't claim to know why the German engineers didn't provide boosted controls for the 109 but I am reminded that Lockheed did exactly that for the elevators on the P-38 to 'solve' compressibility dive recovery issue'.
Boosted elevators worked in the sense that control forces were manageably 'light' - but the airframe somehow lost it's tail in the process. I suspect without proof that neither the 109 aft structure or perhaps the wing structure were designed for high speed asymmetric load conditions that boosted controls would exacerbate.
I do know that Mustang designers provided REVERSE boost to rudder to INCREASE rudder pedal force requirements in dive and slow rolls - as the Mustang controls were too light, relatively speaking for those manuevers - and resulted in overstressing the airframe in certain assymetric load conditions.
The wings could take it, but the aft fuselage I aint sure about. So you could be right.