CC without a save is without a doubt uber. Not disputing that. Add the category of damage via spells and it evens out. A sorc can't buff as well, can't heal as well, can't melee as well... but can damage using mana like all get out.
A sorc can play surrogate healer. Their UMD can get higher than you (apparently) think. However, bard can do it better (we're talking pure classes here, no need to muck things up with MC builds).
We're not comparing apples and oranges. A sorc can't give the
same melee buffs as a bard, and vice versa. You said you could do A, B, C, and D, disregarded E (offensive spellcasting), and asked what other class could do so. I gave an example that was sort of on the weaker end (but nonetheless able to do everything you asked)... the oh-so-obvious answer, of course, would have been "cleric". A cleric wins in two of the four categories you presented (healing and melee), makes a good showing in the other two (buffs and CC), and easily towers over the bard in offensive spellcasting.
Since a cleric wins in 3/5 categories, are they a better jack-of-all-trades?
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