That isn't completely true. Under Khrushchev there was a push to promote "communist self-administration," in line with Khrushchev's absurd boast that the USSR would reach the prerequisites of communism by 1980.
I'll quote from a post I made on /marx/:
The most famous example of ["communist self-administration"] was in the field of law, where Khrushchev encouraged the growth of comrades' courts (which were set up by citizens to hear cases and reach verdicts.) State courts were encouraged to transfer mundane court cases to these comrades' courts.
The idea was that in this way citizens would learn to administer the law on their own, increasingly without the need for the state. To quote from the article "Soviet Comrades'
Courts in Retrospect" by Yoram Gorlizki:
On the other hand, the author notes that, "Many panels and audiences were made up of veterans of war and industrialization who adhered to a harsher prewar puritanical morality and who used the stand offered by comrades' courts to lecture younger offenders, often products of a softer and more liberal post-Stalin society, on traditional Soviet mores. At their worst comrades' courts attracted prigs and busybodies who imposed their own visions of domestic ethics and socially desirable lifestyles on non-comformist youths."
Another aspect of "communist self-administration" applied to law was the setting up of volunteer squads (druzhina) by local soviets, party, Komsomol and trade union branches to patrol the streets independently of the police. Most of these volunteers were young, and to quote one author, "The young druzhinnik, equipped with a red armband and a wide but ill-defined authority, may contribute to maintaining public order; but he may also terrorize his contemporaries." ("Law Enforcement, Social Control and the Withering of the State: Recent Soviet Experience" by Darrell P. Hammer)
The same author gives their competences: "The patrol's duty is to maintain order, and to do this it has the right to warn those who disturb the peace. Beyond this, the patrol may demand to see one's documents. In more serious cases the patrol may write a statement of the violation, naming names and giving the testimony of witnesses. . . to one's employer or to the police, and may eventually be taken up by a comrades' court. Technically the patrol does not have the right of arrest. It does, however, have the right, in 'cases of necessity', to detain a citizen at druzhina headquarters or turn him over to the police."
Many, especially the young, found the druzhina to be intrusive.
While comrades' courts and druzhina continued to exist after Khrushchev, their activities were reined in and given a more "formal" character, with Soviet authors pointing out that talk of the withering away of the state was obviously still premature.