Keep in mind that recording in a studio, where you layer the instruments and balance the levels to the desired result, plus get to redo your vocals until you achieve the desired "take"...
v.s. performing live with a live sound system where there is a mix but things still lack the analog tape "warmth" of classic recording...
is comparing apples and oranges. Plus, the singers used in that film, which was a tribute to The Band, weren't the ideal selections for the songs they were given (song style, song key, vocal range written for someone else).
This is also why being a cover musician is more difficult than being an original musician. Originals let you have your sound, with songs that are tailored to you and your style. Covering music means you have to be able to perform in the styles of many other people (if you're approaching it the traditional way).
As an example, these people in the following videos aren't "the best of the best possible singers to find for the Motown material, within their country", just groups of people in their local areas that decided to work together (with a limited size band covering the orchestra-sized group from records, taking liberties in the arrangement to play to their smaller-sized strengths) to come pretty close doing it live, which is a lot harder than in the studio.
So imagine who could be found for the "ideal remakes" of Motown classic if such an undertaking was done. Of course they wouldn't be out to take away your or my favorite version from history, but they could do justice to the songs if they had the right production behind them to do the material (for them) properly (not trying to do a range of styles), and not as a live money-making venture they financed out of their own pockets.
I feel the music of Motown and Stax is wonderful and should be celebrated, starting in its classic form.