I'll address the middle part about context. This is 100% why you don't take context into account....Here is a real life example.
Luis Castillo had negative value to Cincy when traded. They weren't making the playoffs, and he cost real money. Each start for him was one they couldn't use on someone else to gain information about them.
He had extreme value to Sea, MN, and NYY....as they didn't have 3 very good / great starters for the playoffs. He had less value to LAD and HOU, since they had "enough" starters for the playoffs.
that's why you take context out, why you use some generic replacement player. WAR isn't about VALUE at all. It is a tool to measure the outcomes produced by players so you can compare the outcome produced.
Here is another way it isn't about value / context. Burnes likely produces more WAR next year than Peralta. But, Peralta has A LOT of control left at a low cost. He's going to cost more to acquire than Burnes for those reasons. WAR isn't a tool for measuring that. It ignores that context. If you want it to do more than it is made to do, well, it won't, because it isn't made to do that.