Whether it's a song-based or singer-based approach, you can't say that one is better than the other - they're just different, and serve different purposes. You may prefer one over the other, but that's a personal choice.

Virtually all other published recordings including VOTP should be viewed as samplers rather than definitive studies. It comes back to the pragmatic rather than academic. As so often, you're criticising something for not being what it was never intended to be.

If you want to study these singers in depth, you need to got C#House or wherever to listen to the all original recordings. For most of us, the published versions, selective as they inevitably must be, are sufficient.