I'm A Banana
Potassium-Rich
All but one of my sorcerers have had the opposite approach, why waste your magic for destructive purposes, which you can replicate just fine with weapons, when you could use it for truly fun and wonderous stuff?
Yeah, I don't really follow that logic. Cantrips almost literally can't get wasted. I could blast bolts of fire every six minutes every day, and I'm more accurate with that then I would be with a limited amount of arrows. Getting up in something's face seems reckless, and swords cost money and my blasts of fire do not. Magic is not a precious resource for a sorcerer (or for anyone else who casts cantrips, for that matter).
Changing size, enduring the elements, moving faster, creating illusions, summoning talking birds and shadowy ponies, there's just so much weird and fun stuff to do with magic to just limit yourself to one thousand ways to fry a kobold.
Meh, you really just need one cantrip that blows stuff up and that is almost always a much better choice than any piece of steel.
I've always taken the chance to make a sorcerer's spell list an extension of her personality, always taking advantage of the basic proficiencies to carry the slack in combat -and those basic proficiencies reinforced the peasant nature of the sorcerer versus the privileged detached nature of wizards. To me those profs were part of the sorcerer identity, and without them the class feels incomplete as if it lost something important.
The concept of my gnome was to make a character influenced by the nonsense of Lewis Carroll, using as many random mechanical elements as possible, and it does that quite well (someday, I will make a Wand of Wonder!). I don't feel like he's lacking anything by not being able to summon a shadow pony or use a spear. I've got PLENTY of spells to choose from, even with a second (dragon) sorcerer in the party, so we don't overlap at all really (he got Fear, I got Hypnotic Pattern, we're both in character without overlapping).
I think perhaps your view of a sorcerer's identity is too narrow, if it is not able to embrace different proficiencies without collapsing. Proficiencies don't define a character very strictly.