Symmetra's ability to stay alive during that encounter is why her smaller frame is important.
Not her damage, which would be completely irrelevant if she dies before she builds it up. Head to head, without strafing, D.Va murders Ms. Satya. Similarly, D.Va will not hit an up-close, strafing Winston 100%, while he will not suffer in the same manner. D.Va's movement penalty is a primary reason Winston (or Sym) is able to go toe to toe with her higher damage output.
In a 1v1 fight, Symmetra isn't even that strong versus D.Va, but where her strength lies is her damage output (which is more than twice as high as winston's at full charge). I don't even know this game where you think a symmetra can just run around a d.va and not get killed most of the time. Because a D.Va who can aim can demolish a symmetra before she hits level 3 charge. Keep in mind that D.VA doesn't have to move when fighting winston or symmetra, they both need to be in range of her weapon. And D.Va just out DPSes a Symmetra within her beam range.
And I can beat a Bastion who isn't having a great day as Winston, either. I am not going to suggest Winston is at all ideal to deal with that hero, though. That you're not even acknowledging how easy it is for a Symmetra to sashay in circles around D.Va tells me you haven't had to deal with that very much. A shielding Reinhardt or a D.Va up close is just a large target to fuel her photon gun levels and not much of an urgent threat.
This is the kind of player it seems like you're talking about when it comes to d.va
https://www.youtube.com/watch?v=ZKyjD4s5SoE - that is a long time to down a d.va. Someone with aim only has to hit her for 200 health? That's not hard with proper tracking skills..
But of course if your d.va aim is like the video, then of course that D.Va is not a threat. But against a D.VA that can aim, D.VA can kill her before she even hits level 3 and she doesn't even instantly win when she hits level 3. Armor also apparently cuts her level 3 down from 120 dps to 80.
Where symmetra shines against d.va is not in a 1v1 run around scenario. It's where symmetra is already fighting at an advantage and can contribute a lot of damage to both mech and d.va without having to worry about being gunned down or having her damage blocked by defense matrix.
BTW, auto aim isn't worth a damn vs d.va's mech since it's so huge you don't even need auto-aim to hit her at close range. And good players will easily hit you back at that range, it's the same thing with winston. SUre perhaps a bad winston beats a bad d.va, but d.va with aim simply out damages and outlasts winstn. She wins that fight almost every time, even if she doesn't get the kill.
edit:
Yes, got a bit off topic but think about winston in symmetra's shoes. He is just a huge target, less dps... Symmetra at least has the dps to down the mech while winston simply doesn't.