I think the premise is mistaken. Very short answer..

Khrushchev's proposal involved giving the GDR control over the access routes between west Germany and west Berlin, also insisting the western allied powers pull out of west Berlin.

Michael Beschloss, "The Crisis Years, Kennedy and Khrushchev 1960-1963", here talking about Khrushchev's proposal from 1958:

Khrushchev’s peace treaty was designed to compel the Western powers to recognize two German states, sanctioning the division of Germany and Europe. Berlin would become a “free city.” Stripped of its twenty-five thousand Western troops, it would naturally fall into the Soviet sphere.

Such an accord would cauterize the growing exodus of refugees to the West and buttress Soviet power in Eastern Europe. A peace treaty on Soviet terms would undermine faith in other Western guarantees and demonstrate to the uncommitted nations that the Soviet bloc was indeed the rising force in the world. It would make reunification of Germany less likely, which would suit Khrushchev just fine.

Maybe the confusion stems from the fact that after Khrushchev issued his ultimatum, Gromyko prepared two treaty drafts, one of which was with the GDR alone?

From: KHRUSHCHEV AND THE BERLIN CRISIS (1958-1962)VLADISLAV M. ZUBOK Working Paper No. 6 :(https://www.wilsoncenter.org/sites/default/files/media/documents/publication/ACFB7D.pdf)

Two weeks later Khrushchev in two speeches presented the West with a choice: either the German peace treaty would be signed by all former Allies with occupation rights in Germany, or the Soviet Union would do it alone by reaching a separate treaty with the GDR.

The new documentation shows that Khrushchev's ultimatum was ninety percent improvisation. Not until a month after the speeches, on Christmas Eve of 1958, did Andrei Gromyko prepare two drafts of a German peace treaty. One was with the GDR alone. Another, with two German states, was designed to achieve a partial withdrawal of foreign troops from German territory, which "would be effectively tantamount to a collapse of NATO." Gromyko added matter-of-factly that "Western powers and the FRG obviously will not agree with our proposals." Betraying the design of Khrushchev, he concluded that "after the possibilities of political struggle with the whole Germany will be sufficiently exhausted," the Soviets might conclude a separate treaty with Ulbricht and Otto Grotewohl, the GDR prime minister.

Also, gradually after 1961, East Berlin was integrated into the GDR, against the protests of the western Allied powers.