In reality it is estimated that anywhere between 50-70% of all Red Army tanks were inoperable at the outset of Barbarossa, most due to poor maintenance and lack of spare parts.
This is a falsehood which I've covered on page 1 of this thread.
Yes, this is really the right moment. If the USSR had at least a month to mobilize like France, this could turn the war significantly. The USSR began momilization just a few days before the war, and the Army was split into three echelons - on the border, on the way to the border, and just started to move towards the border. If the decision to mobilize had been made a month before the war. Then there would be more troops on the border, they would have had time to prepare positions (trenches, fortifications, AA and AT defenses, organize a front line), tanks would not enter battle in small groups and there would be fuel for them. In reality, the concentration of troops on the border is a precedent for starting a war, the game does not simulate this issue. And you can concentrate your entire army on the border and this will not have any diplomatic, economic or military consequences.
I think you overestimate the Red Army here. Mobilising earlier could've well resulted in more troops being encircled at the border, and maybe an earlier Barbarossa.
Kotkin straight up calls a few of Stalin's generals idiots, for wanting to move forces straight to the border just prior to the German attack. It was fortunate for Stalin that he only agreed to this in a limited scope.