Pathfinder Tool Precision in Web Mode

True enough: it is indeed very small. But, if you're working on creating an icon and you want it to be clean at 16px . 16px, you might want to create it at that specific size at which size the 0,028 pt will have an impact. Of course, I could create my shape at a much bigger size and then scale it down, but the fact is that it still doesn't answer my question.

Your guess about the hardware performance thing might be the right answer, but I would have like to get an official anwser from Adobe themselves.

These options were already unchecked actually.

And I feel like it is not what's causing the issue since creating a new document and unchecking these options doesn't change anything to the 0,028 pt unprecise default setting. If I go ahead and change that to 0, then I get 0,001 pt as a vallue for that setting (0 doesn't seems to be accepted as a vallue), which solves the issue.

But, we are talking about getting rid of the bug here, which I know how to do. My question was: why does that precision setting exist in the first place? I don't see how it can be useful in any way. I mean, who might want to have the pathfinder tools not to be perfectly precise?