Though Oblivion's save system wasn't bad, this would be an improvement.
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The only real con I'm reading is "It's not really necessary". And I agree, we could easily do without it. But that's no proper reason not to add this improvement. The other cons are just from people who completely misunderstood the suggestion in the first place.
Pretty much every improvement in anything could be considered unnecessary, so I agree that it is an extremely weak argument against the suggested feature.
Organizing save-games by character would be useful if on each "character save page", there could be summaries of the character's most recent quests, their specializations, journal entries, etc.
I'd love an integrated "manage save-games by character" feature since this was severely lacking in Oblivion.
Once I got to saves in the multiple hundreds, not having the ability to name each save-game made things cumbersome.
I could have kept a hand-written chart, but an in-game manager would be much more efficient.