It would certainly be similar in this regard - even down to the geography. But not nearly as bad as "Canada Goose."
Personally, I cut Winter Wren a bit of slack because the name is at least descriptive. The taxon sensu stricto is the one that would "appear" in a great portion of its range in winter. That descriptor never really made sense for the Pacific Wren populations before or after the split, so I could argue that the "true" winter wrens retained their mantle. But to your point, that does not alleviate the pre- and post-split naming confusion and I'll concede that.
And obviously, there is nearly nothing "Nashvillian" about a Nashville Warbler other than where Alexander Wilson first saw one (and Tennessee Warbler was already taken!). The only really valid argument for this name is tradition, or what some call "stability" - but you and I just pointed out examples where that argument seems to take precedent over others.