Trotsky was a radical but he wasn't the kind to purge every single person who has a remote chance of deposing him, he wouldn't send that much persons to gulags or purge the army; Trotsky isn't some kind of maniac communist, he's very capable of rational decisions, he wouldn't invade all of Europe just to spread communism, he would only support communist movements; that's better than Stalin, obviously it will still not be the paradise Marx theorized but what do you expect from the Bolsheviks?
Trotski was a communist, that alone is extreme enough. Defenitly he would sent milions in the slavery Gullag system , his ''buddy'' Lenin started the system. Trosky led the Red Army during the civil war and was sucsesfull manly due to his extrmism and ruthlesness. It would be naive to think that the Sovjet Union would be even marginal better under Trotsky than under Stalin. Or that coomunism would be less expansionist under Trotsky than under Stalin.
I would think a Sovjet Union under Trotsky woul be even more expansionist in Europe and USA than under Stalin and dangerous. Stalin didn't like the possibility that , by exaple a Communist France or Germany would be more succesful than his Sovjet Union.
The communistic system disregard life and individuals. Trotsky would be the same insane dictator as Stalin, Mao, Pol Pot and all the other comunist dictators. Will there not be milions sent in a slavery system as the Gulag than milions will perrish in insane economic and or agricultural experiments.
Lenin, Trotsky are extremist Stalin was more gangster, never the less they disregard life of humans in the name of their extremist world view.