It seems to me that being forced to leave the USSR in 1972 was more of a reward than a punishment, and potentially embarrassing for the USSR. Why did the Soviets want him to leave, instead of sending him to a gulag to die, away from the public eye?
the GULag did not exist in 1972.
he was no dissident.
he was sentenced to community service for unemployment and the distribution of pornography (his poems occasionally would involve genitalia) and this story was picked up by the BBC as he would persist that he was, in fact, a poet by vocation and not umemployed. The moral of the story for the Western viewer was "there's no freedom of artistic expression in the USSR!!!"
Solomon Volkov in his "Magical Chorus" book on Russian 20th century culture explains that the Soviet Authorities presumed the exiled artists would soon grow sick of the squalor and oblivion in very bottoms of the Western society and return to the USSR more patriotic than ever (or cease at any rate to have a harmful influence at home). This is how it worked for Russian Revolution era exiles as Alexandr Vertinskiy, Marina Tsvetayeva and Ivan Bilibin. Of this new generation not many returned but, indeed, they tasted poverty and would committ suicide (Alexander Galich) or become savagely patriotic for the Soviet Union (Eduard Limonov). Others again - Voynovich, Brodsky, Dovlatov - sought jobs in Anti-Soviet propaganda (Deutsche Welle, BBC, Radio Free Europe) and were judged reliable enough to get some random posts in Western Universities.