I think you vastly underestimate the capabilities of the Soviet to organise a defence and the quality of that defence as well as vastly overestimate Kornilov's chances. The Interdistrict Committee of the Soviets established the Committee for Struggle against the Counter Revolution which was operation and organising the defence before the Provisional Government had even put out the word for the soldiers to assemble. Vikzhel, the railway workers union, worked to prevent signals and messages being sent by Kornilov to his troops, as well as diverting the trains carrying his troops and organise trains to carry the Petrograd Garrison troops loyal to the Soviet to defensive positions. Practically overnight the Bolsheviks and their allies managed to assemble a Red Guard militia of nearly 40,000 workers, arm them, organise them into detachments, and give them orders. The workers often dressed in their best clothes, their church clothes, and put up posters proclaiming discipline and against drunkenness. The suburbs of Petrograd became a military camp, workers dug trenches, laid barbed wire across intersections, built barricades and bunkers. The Petrograd Garrison, over 100,000 troops, either proclaimed their solidarity to the cause and joined the defence or they proclaimed their neutrality. Nearly 20,000 sailors armed from Kronstadt joined the defence as well and soldiers from Estonia, Finland, and Latvia sent messages of solidarity and prepared to organise to come to Petrograd's aid. The Soviet sent out delegates to meet with Kornilov's troops at Luga and soon even the Cossacks were flying the red flag with Kornilov's army disintegrating the moment they realised what they were being organised for.
Actually, it was General Alexeev who said of Kornilov that he has, "the heart of a lion, the brains of a sheep". Brusilov said of him, "The chief of a bold guerrilla band and nothing more..." Pavel Miliuikov, leader of the Kadets, said that Kornilov had a "childish trust in people who knew how to flatter him". Most damning, perhaps, is his former superior General Martynov's assessment of the man was that he was "an absolute ignoramus in the realm of politics". Martynov said that, "he lacked organising ability and with his violent temper and lack of equilibrium was little fitted for planned activity". Kornilov was, by all accounts, bold and well liked by the right-wing officers and soldiers around him, a poor strategic commander, a brutal disciplinarian, incapable in the realm of politics, and a puppet to other interests.