The downsides to that are that you don't get any Invocations (no Cha to damage, and no attacking with Pact weapon twice), and Dark One's Blessing suffers (it is based on your Warlock level). You'd also sacrifice having some ranged utility, in that you can't Agonizing Blast your Eldritch Blast (+Cha damage Eldritch blast) until you take Warlock 5, Devil's Sight gives you 120ft vision in Magical/Non-magical darkness, which is very useful.
I mean, it's much of a muchness, really. I know Sorcerer 13 gives you a 7th level spell, but if you're goal is to hit things hard, what is it about 7th level that is good? For an "occult" feeling, maybe Finger of Death 1/long rest? Teleport for utility? But honestly? Given the role, Paladin 6/Sorcerer 4/Warlock 2/Sorcerer +8 means it can hit even harder in combat.
+Cha to hit, (+Wis and 2xCha) to damage with a Dragon, and it kicks off doing that at level 10.