Yes but thematically the 4e sorcerer is a blaster, just like the 5e sorcerer...
No, thematically the 4e sorcerer was, just as the 3.5 and 5e sorcerers are, an innate arcane-magic-user with some sort of magical heritage providing the power. In the Role sense, it was a Striker. And the 3e Sorcerer was often played as a sort of 'blaster' (though that wasn't exactly optimal in 3e, but then neither was picking a Tier 2 Sorcerer over a Tier 1 Wizard in the first place).
and while everyone was made to hold their own in combat... some classes got features like extra skills, ritual caster, and a wide breath of non-combat utility powers to go in a more non-combat direction
Not so much that last, but an extra skill or two or Ritual Caster, sure - but that was only the equivalent of a couple of feats. As in 5e, 4e characters were OK out of combat by default, because their checks, between stats & leveling, would mostly be adequate to participate.
Again the 5e sorcerer seems to pull it's inspiration from 4e as opposed to 3e... which seems to be the disconnect some people are having with the 5e sorcerer not meeting their expectations.
No, 4e & 5e inspiration was from the original sorcerer concept - they just didn't take the biggest mechanical support (or reason, I suppose) for that concept: Spontaneous Casting.
Mechanically-supported? None of that was mechanically supported. Trigger her berserk button and she'll target you exclusively at the expense of all else.
And if what she targets you with isn't up to snuff, it won't matter.
Underestimate her and she'll have something to say when she defeats you.
And if the mechanics make her weak enough that it's not
underestimation, oh well, that whole 'defining' aspect of her personality is lost, or, at least, defined a little differently, more as comic relief...
So, yes, mechanics can matter even to RP definitions of your character. Even were that not the case, the obvious and never-disputed fact that you can define your character via RP
does not mean that its abilities cannot also be defining.