The point is: usually we do not know in advance whether it is possible or not to change a given initial problem solver in a provably good way. The traditional approach is to invest human research effort into finding out. A Gödel machine, however, can do this by itself, without essential limits apart from those of computability and provability.
Note that to prove a target theorem, a proof technique does not necessarily have to compute the true expected utilities of switching and not switching--it just needs to determine which is higher. For example, it may be easy to prove that speeding up a subroutine of the proof searcher by a factor of 2 will certainly be worth the negligible (compared to lifetime ) time needed to execute the subroutine-changing algorithm, no matter what is the precise utility of the switch.