The more people are involved, the more interest the state has in private property.
This is why for example we have employment and health laws.
Marsh vs. Alabama wasn’t decided because it affected a lot of people. It was decided that way because it was about a private company who literally ran an entire town. It was decided that because they were performing the functions of the government, the rules applied to the government should apply to them.
Since then, Marsh v. Alabama has been “limited to the facts.” Later precedent has clarified that state action only applies in cases where private actors take up duties that are “traditionally exclusive to the state” (Manhattan Community Access v. Halleck). No matter which way you slice it, AWS does not fall under this precedent.
If I buy every ticket in Yankee stadium and turn it into a rally for Some political issue, is the management required to just deal with it? What law requires that AWS host people who want to overthrow the government?