And yet, MMGs were included in the list... The Vickers was available before WWI. It was a relatively light machine gun, particularly compared to the Maxims. If the US is looking at foreign designed guns, I cannot see the Vickers not being included in the list, unless there is an obvious bias against British guns...
Neither the Lewis or Vickers are available much less available in 30.06 pre WW1. The Lewis which at the time is in no way production ready is not invented until 1911 and the offer to the US is really give me money to develop this and I will sell it to you, which gets Lewis kicked out of office. he then goes to FN and BSA who are willing to turn the concept into a manufacturable gun and give Lewis a licence fee.
The Vickers is only accepted into service in 1912 and the BEF goes into France using Maxims ( and Hotchkiss Portative) and the Belgians field a total of 20 Lewis ( which is not accepted into British Service until October 1915 btw)
As soon as you get WW1 the US does not get a look in with any European manufacturing.
There actually is a strategic choice the US makes in April 1917 as to whether to buy British or French. Now as the French are the biggest most experienced army with most written down in 1916 - its the 1916 manual that the US is choosing it then makes sense to use the 75/105/155 Hotchkiss Chauchat suite, the rifles you can't and even the French are unhappy with theirs.
Also bear in mind that apart from the rifles this means buying them now and making them later ( 1942 as it turns out).
Could they have gone for the 18lb/4,5/60lb Lewis Vickers route, maybe, they are in inches and all the manuals in English anyway. Its feasible but they would be using the MGs in .303 ( as they were using the French weapons in 8mm initially) and given the performance of US arms industry in the period that's what you got.
Does that make a long term difference. well it probably kills off the BAR if you have a Lewis in 30.06 which BSA had told you how to do if people had bothered to read the technical package what do you need the BAR for. But once again does that mean the US has enough combat experience to decide that building a squad around an LMG and ammo carriers with some infantry and grenadiers is a better option than building it around a semi auto rifle and grenadiers. Probably not really.
What you may have is John Browning treading the well worn path to Liege and selling his ideas to FN resulting an a Browning in the 20s/30s with belt feed and interchangeable barrels which then becomes a race between the 30.06 Lewis, the Jonson, and whether the US can rechamber an 8mm FNFM ( fusil-mitrailleur) or Bren to 30.06 or whether they spend money interwar on their own LMG. But dont order any.
The Madsen suffers from looking like a Bren, its not an LMG cant fire enough, its a heavy semi auto rifle with limited burst fire fine for a fixed position useless for carrying around a battlefield until the 20s when they fix the sustained fire but by then its competing with guns designed to do that from the get go.