Orcus on a bad hair day
Challenge accepted. I'll give you spells that do it directly, spells that do it by adding on, and then show that the spell damage is even more than that.Is there any level that casting burning hands in a level 1 or 2 slot actually becomes better than an attack action with my proposal?
First, a list of ones with either area of effect or repeating damage that do more.
Burning Hands - your sample. At 5th with two target that's 8d6 damage. Equivalent to 2d6+7 great sword with Extra Attack which is pretty good at 5th. Catch more than two in the 15' cone and you'll do a lot more.
Flaming Sphere (bonus action repeat means a single casting will add up to way more than a single Attack action)
Heat Metal (same as Flaming Sphere)
Magic Missile (3x 2d4+1 with no chance to miss is more than an Attack action once you consider miss chance.)
Scorching Ray (3 x 3d6 works out to be two attacks of a greatsword doing 2d6+8. +8 is nice bonus damage to be doing at 5th. 9d6 blows sneak attack out fo the water).
Shatter (with multiple foes in a 20' diameter)
Spike Growth (debatable. stepping on one square isn't more than an attack action. But cast in a hallway where someone needs to go across 40' of it will add +8d4 (avg 20) at 5th, +16d4 (40) at 11th, and +24d4 (60) at 17th.)
Then there are the ones that stack with other actions by only being a bonus action to cast:
Hellish Rebuke (well, reaction to cast in this case)
Spiritual Weapon (like Heat Metal, but just a bonus action to initiate to it always wills stack)
All 1-2 level paladin smite spells
And don't forget the ranger and the warlock's damage adjusters of Hunter's Mark and Hex - those will start adding a heck of a lot more damage.
(This is just looking at PHB spells quickly, I tossed a lot of "nicer but not nicer enough", nor did I look through XGtE)
Now let's multiply that that many leveled damage spells still do half damage on a successful save. So even if the succcess damage is similar to an Attack action, the expected damage is greater since attacks do nothing on miss.
And finally, let's remember that it's about the damage done, not just the dice. Due to the nature of only two proficient saves, even with good ability scores most foes will have 2-4 good saves total. So having a wider selection of worthwhile damage spells means a wider ability to pick the save (and damage type) that is best against a particular foe. So while hitting remains roughly static with bounded accuracy over levels, an increasing DC vs. a flat save makes that damage spells with saves will get more likely to do their full damage if you have a big enough pool to have the right type of save - and this makes it that you will.
Again, I'm fine with spells doing more than attacks - this is just showing that making low level spells viable damage dealers at higher levels means that more actions per day will be > attacks with fewer level for cantrips doing < attacks, so the average damage for the caster will improve above weapon attacker ranges.
The point isn't about any particular spell, it's about replacing < weapon Actions (cantrips) with > weapon Actions (now-viable low level damage spells) over the course of a day raising the average.