It's really just a consequence of multiple WW1 era decisions.

The "06" in the name .30-06 means 1906. That cartridge was made for the standard issue Springfield rifle to compete with other similar European cartridges. This is the rifle that Americans took to war in WW1. However, the US army didn't really use machine guns at that time. It was a rapid necessary adoption, first with foreign weapons and then new weapons made by Browning: the M1917 machine gun and the M1918 (BAR).

Understandably those guns were chambered to fire the same cartridge already being mass-produced for the infantry rifles. Now you have 3 guns in WW1 using the same .30-06.

Between WW1 and WW2 was the development of a semi-auto rifle to replace the Springfield. The Pedersen rifle, a weapon that was almost adopted, fired a smaller .276 round. However the Garand could be chambered to fire .30-06 and didn't require special lubricated clips. No lubrication and an existing stockpile of hundreds of millions of rounds of ammo made the decision to keep using the .30-06 pretty easy.

I'm not sure how you mean. The .30-06 had been the standard rifle and light/medium machine gun cartridge since 1906, when it replaced the earlier, round-nosed .30-03. There was an attempt to switch to the intermediate .276 Pedersen in the early 1930s for the new M1 rifle then being designed, but the cash-strapped interwar army could not bring itself to adopt a new cartridge, and so the M1 was produced in .30-06.

For that matter, the .30-06 was never entirely standardized. The US Army employed four main cartridges for infantry weapons during the Second World War: .45 Automatic Colt Pistol, .30 Carbine, .30-06, and .50 Browning Machine Gun.