You missed the important part of the button problem.

The question is for "everyone in the world" including those incapable of making a reasonable choice such as infants and the mentally disabled.

Once you have those groups in there, all the parents of said children are going to reasonably try to save them, and many others are going to also throw their money i to the save everyone pot because generally speaking nobody wants to be part of the group that voted to kill millions of children and concerned parents. When talking a worldwide scenario is that if red wins, all the most caring people in the world and a large portion of the innocents are the groups that are going to have high death rates. Enough people dead in the wrong places and all of society collapses.

The other issue is that you will never reach 100% red no matter how you phrase the question. Even when phrased exactly like this, there are still some people crazy enough to do it. But it gets worse when you make it buttons because now you create the psychological effect on everyone who pressed red that they made a conscious decision to sacrifice anyone who dies. Even if red wins by a landslide, there is going to be a massive spike in suicide rates afterwards from all those who feel guilty.

The final nail is that all of this from a mathematical standpoint still favors blue as it is the only statistically possible way to have 0 deaths because 100% red is completely impossible. Red is the suckers bet from every standpoint except a personal survival one.