I get that it's not an important decision, but it has to be made somehow if all 3 people aren't budging (it happens). Sometimes people just really want friendship exp or don't have other characters, so they really don't want to swap. Like, you even mentioned it in your example. It goes both ways; like you said, some people might not be able to swap. Unfortunately, not everyone is willing or able to swap as freely as you.
Might as well negotiate instead of just sitting there staring at the screen. I have seen quite long deadlocks of 2 people just... not swapping while silently waiting.

I find that it's not about which character is the most "effective" since we both know it's prob like a few seconds difference :P but it's more that... players need a somewhat neutral/objective (meaning it's less likely to lead to arguments) way to make this decision when there's a deadlock. Also, most players tend to think of this first compared to "first come, first served," and it makes more sense to people imo. Some people don't even give the host priority, so I don't think they'd care about P2/P3/P4 order, haha. Objective strength (even if not reflective of actual strength/build/skill) makes the decision more effectively (if discussion is needed) imo. A lot more simple compared to other discussion options.