The chronological argument doesn't work either when you consider the Country Bear Jamboree, which is very much a twentieth-century affair. As long as the exterior of the doesn't look modern or jazzy (and the concept art doesn't suggest it will), the thematic fit will be no worse than with the current version.
(For what it's worth, I will be very sorry to see Splash Mountain go, so I'm not posting this as someone opposed to the current version.)
But what does it evoke? Country Bear Jamboree has songs that although were contemporary at the time of design, were humorous takes and tributes to the times of the covered wagons and advent of the train. That directly matches Walt's words for Frontierland. No one is saying everything is perfect, but those who say princess and the frog are further away have valid points to me. The argument and point is it for time and space but what does it evoke?
Star Tours in Tomorrowland can sound like a horrible fit, the first line is literally a long time ago in a galaxy far far away. That was pretty jarring to both Disneyland which has always been American Mythos, but then you realize it evokes space travel and action akin to buck Rogers serials.
No one is saying Princess and The Frog is the farthest off, but it is certainly further than anything previously a ride or attraction. I see that argument as valid. I see your points as valid, but for some reason you say "doesn't work" "does not make sense to you."
Brer rabbits story in the ride is literally moving along "Time to be.kving along" lines are used for this, and exploring in a time period of the covered wagon and pioneering railroads. I think it would be hard to say that fits Frontierland less than Princess and The Frog 1920s depression theming, but that is just me.