Yes, the Axis have to move fast if their goal is to take down Russia.  The problem is that they aren’t capable of moving fast. Leningrad can be fortified to prevent a naval G2 attack and a land G2 attack is going to be extremely difficult.  On turn 3 Russia can just move their forces out.  That’s part of the issue; If Russia always keeps its forces one move away from Germany with an infantry in between, they can amass a huge force. Germany is stuck moving one space at a time.  Even if you send Japan and Italy against Russia they can’t move very quickly.  Italy can’t get to Iraq until I2, build an IC until I3, build units until I4, and if Britain liberated the persian extra units and merged them with just a few Russian units in North Persia, Italy might not be able to attack Russia until late game.  The same issue occurs with Japan, even if Japan invades Russia and tries to take up as much money as possible, the Russian stack can move one space away all game long. Sure, Russia loses some money, but Japan is going to struggle to effectively fight anyone else.

Bottom line, I’ve played multiple games as the Soviet Union where I didn’t let anyone attack my units except an infantry I left as a road block.  Even when Japan invades Russia turn one/two and tries to keep pushing, it still didn’t make much difference because they can only take a territory a turn.  So when Germany finally reaches Moscow, almost every single unit I’ve built as Russia is there defending my capital.  Sure, if time weren’t a factor, it’s a bad strategy, but I know that the Allies are going to be landing in force by turn 5 or so, so the Axis is not able to deal with the Allied pressure and overcome a huge Moscow stack.

“Britain can be taken out of the game or just contained.”
Scramble your fighters west of London when Germany attacks; Save the transport/maybe the destroyer.  Make sure to save your fighters.  Move whatever forces you have left to Canada. Build your ships in Canada for a few turns. Move up to the SZ west of London and build more ships there. Use your fighters as a deterrent because they can scramble.  Have a few US warships join this squadron at the same time they move to off the coast of London. A threatened Sealion complicates this, but the infantry that will be built to defend London can be used for amphibious assaults later on.  Paired with the three/four fighters that were saved, its a pretty powerful landing force.

“Italy can move into Russia via the Middle East.”
If they ignore Egypt/clearing the med.  If they spend the time and money going into Egypt, it’s going to be fairly late in the game by the time they get any sizable force through the Middle East and into Russia.

“The USA could be kept busy by Japan in the Pacific.”
With all of America’s money and two rounds of building before war, surely America can spare two/three transports a turn and a warship or two (since they already have a warship in the Atlantic).

“Germany can push for a G2 assault on Leningrad (especially if turteling)”
Fortify Leningrad from an attack from the sea.  When Germany attacks by land just move all those units back to Moscow via Archangel.  If Germany attacks G2 make sure they can’t hit you by sea.  If they hit you over land on G2 all they have is their starting units and 5 newly built tanks. As long as you keep Leningrad fortified, Germany can’t hit you G2 with any real force.

“Japan can move into Russia to also eat away of those 1 IPC zones.”
They have 18 infantry to contend with.  They can take a handful of territories in the far east, but doing so gives Russia a 12 IPC bonus.  It will take 2 turns of income before it pays off.  If Japan only takes a handful of Russian territories, it won’t make a difference until later in the game.  Additionally, Japan needs land units to go into China. So any units that are used to take and hold Russian territory aren’t being used to fight the Chinese.  If Japan tries to march through Russia, Russia can move one step back every turn.  This will lose money for Russia, but Japan will have tied down a large number of forces allowing the Pacific Allies a chance to gain momentum.

A big part of the problem is that infantry defend at a 2 and tanks attack at a 3, so it takes about 8 tanks to match 10 infantry in a fight (infantry soak up hits better than tanks).  If you consider the fact that russia is probably going to have 30+ normal income for at least 3 turns (plus the the lend/lease NO for a few turns after that, depending on when Germany attacks), Russia can build 10 infantry in Moscow for probably five turns.  This means that Germany has to match that with 8 tanks or 48 IPCs EVERY turn. Not to mention that Russia builds their infantry in Moscow and Germany builds its tanks in Berlin a couple turns away. Maybe on turn four or five Germany can build in Ukraine or Leningrad/Stalingrad, but even then the tanks aren’t within striking distance of Moscow.

Some of you have said to just go around Moscow and soak up territory, except Russia can block you with one infantry every step of the way.  Even if Italy takes out that one infantry, only tanks and mech can blitz, so Germany will have left all the original infantry and art. behind.  A stack of tanks with only a handful of mech for fodder is going to get ripped to shreds.  And where is Italy getting the units to send to the eastern front?  They start out broke and have to spend all their money in the med just to get any NOs.  Furthermore, even if Germany can grab all this territory, Britain and the USA are going to be landing a dozen units or so every turn in Europe past turn five or six.  Most of Germany’s newly gained money is going to be spent fending off the allies in Europe.