Basically at low levels you cast 1 Burning Hands per encounter when you can catch 2 or 3 opponents in it and then plink with a longbow, crossbow or cantrip. It feels lame when you're not using Burning Hands, but you're actually statistically on par with or slightly ahead of the Fighter.
Yeah, don't buy this.
If NPCs need to roll a 13 to save against Burning Hands, it does an average of 8.6 damage per foe (less against better foes).
As seen earlier, the low level two weapon or two handed weapon fighter tends to do about twice as much damage as a wizard from round to round.
So with 3 foes in a cone (which should be somewhat rare due to the narrowness of 53 degrees of the cone, hence generous) and a 3 round fight and a wizard using light crossbow with a 16 Dex (also a bit generous):
Wizard: 2 rounds of 4.075 DPR plus 1 round of 25.8 DPR = 11.32 DPR
Fighter: 3 rounds of 8.15 DPR
So, the wizard does an average of 9 additional points of damage. If the wizard only caught 2 foes in the Burning Hands, then they did about equal damage.
Now lets look at a 3 round encounter where the wizard does not using Burning Hands:
Wizard: 3 rounds of 4.075 DPR
Fighter: 3 rounds of 8.15 DPR
The fighter does an average of 12 additional points of damage.
And many players of wizards are probably casting Mage Armor which uses up one of his spells. If not, he is practically toast for anyone attacking him.
At level two, the wizard gets another first level spell. The fighter gets Action Surge. So now for many players, they can get two Burning Hands (after a short rest) whereas the fighter gets two Action Surges (after a short rest).
Granted, at second level, an Evoker can sculpt spells and may be able to get an additional foe into Burning Hands by blasting through the front ranks, but most wizards cannot.
No doubt. Higher level wizard can nova a lot more than this, but at low level, sorry, but fighters rule.