The "Museum" kinda plays on the assumption by DN that the only reason anyone would consider saving Chloe is their personal emotional attachment to her, and it's not the only available argument at all.

Devs basically said in one of the interviews that attachment to Chloe and building special relationship between these two is "requerment" for wanting to save her in the first place. Which sounds logical.

Meanwhile, it basically beats at you from all sides to convince you to kill her.

No, this guy from the video that you linked was not the only one who paid attention to the themes/lessons and technical aspects of time travel. The fifth episode alone was able to convince many fans that using 'these amazing powers was a bad idea. Regardless of attachment to characters. I was one of the guys who was completely sure that the jump from the diner would be the last. And as we have seen, Max fully supports this approach.