Godel's comments about the "true reason" for incompleteness

"The true source of the incompleteness attaching to all formal systems
of mathematics, is to be found---as will be shown in Part II of this
essay---in the fact that the formation of ever higher types can be
continued into the transfinite (c.f., D. Hilbert, 'Über das
Unendliche', Math. Ann. 95, p. 184), whereas in every formal system at
most denumerably many types occur. It can be shown, that is, that the
undecidable propositions here presented become always become decidable
by the adjunction of suitable higher types. A similar result also
holds for the axiom system of set theory."

This comment by Godel has me confused, first of all by what he means
by "true source". Isn't his proof and later refinements/
generalisations of it a "true source" for incompleteness? Also, I was
under the impression that the whole point of Godel's theorem is that
any kind of proof procedure or list of proof procedures that you can
*even indicate* will not be able to decide all mathematical
propositions. It sounds as if he is saying "ah, we can just continue
adjoining higher types in such and such a manner, and eventually
arbitrary statements become decidable (i.e. for any statement, it
eventually becomes decidable)". I thought the whole point of Godel was
that even if you spent a billion years outlining precisely a method of
coming up with formal systems, there would still be propositions that
could not be resolved by any of those formal systems.
.

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