From: Living in the fair city of Melbourne, Australia
The problem is that the early war Soviet supply situation is pretty awful, without much the player can do about it, so ready units will be even more scarce in the first couple of turns than they are now, which could cause Soviet lines to implode quickly.
Due to the higher Axis morale and likely TOE%, it will only theoretically affect the Axis as much as the Soviets, at least initially.
There's not much either side can do to iron out supply difficulties in a certain area, as the only way the logistics system can be influenced is through air transporting supplies or HQ build-up.
Supply being a part of the equation would require more player control over where supplies end up.
If I have understood "unready" status right, it doesn't entail anything to units defending, it just precludes them from attacking. So, in principle, I don't see any reasons for that alone being a cause for Soviet lines to implode. It would certainly make more difficult for the Soviet player to launch counterstrokes, at least until the RKKA supply network starts to work as vehicles get mobilized from the civil sector and produced.
About the effect on the Axis. It will certainly have an impact on how long can panzer spearheads sustain intensive offensive operations if not managed through air drop or HQ build up, as you say. Tools which, especially on the second case, are perhaps a bit too severe on the "global" penalizations they entail. On the other hand, I don't see a case for having rules modelling German trucks lack of endurance - and thus increased attrition. For the Soviets, there are, at least until they get US Studebackers.
And finally, yes, I agree with you that one thing missing in WiTE is more control on how supplies flow to the units (I think Tarhunnas commented on that elsewhere).
Perhaps "Refit" mode could accomodate that, perhaps not: would it make sense that units in refit, not only receive replacements first, but also get their supply needs satisfied "first"?