Well, at least for me, it's really difficult to invest into multiple characters as much as I wish to invest in a character. As in, I would really, really struggle with that. Having a stable of characters would push me hard toward a pure pawn-stance game, and I don't really get much enjoyment out of that perspective on play.
It would be like asking an actor to play a main character in not just one show, but half a dozen shows, simultaneously. Some really good actors are probably quite capable of that. Most, however, would quail at the schedule requirements and might run into issues with performing so many entirely different people consistently, especially with long gaps between different performances.
Having a stable of PCs is a valid and even wise approach for old-school styles of play. It isn't really compatible with the styles of play that interest me. If D&D purports to serve all those styles--as it clearly does, what with cooperating with Critical Role and other highly-narrative, long-form D&D podcast series--then it cannot be designed predicated on the idea that each player definitely will have a stable of PCs so that any single one dying is "easy come, easy go."
I do think that, perhaps as a more advanced optional rule, (maybe something in an early major supplement? Or a freely-available conversion-guide type thing?) it would be good to have rules for how to very quickly draft up a reasonably effective PC for various classes. That would help support players who prefer the "character stable" approach, without mandating that people use that approach.