Gravity at large scales: force hierarchy or charge cancellation?

[Roberto Pavani]

TL;DR

Gravity dominates at cosmological scales even though it is not stronger than electromagnetis, simply because matter is electrically neutral on average?

We know that gravity is much weaker than electromagnetism at the particle level (~10⁻³⁶ ratio).
Yet gravity is the dominant interaction at cosmological scales.
It seems to me that the explanation (my naive one) is straightforward: matter is electrically neutral on average, so EM fields from different sources cancel at large distances. Gravity, having no negative "charge," accumulates without cancellation.
If this is correct, then the so-called "hierarchy problem" between gravity and EM is not really about the coupling constants themselves, but about the statistical distribution of charges in the universe.
Is this view standard/accepted/discussed, or am I oversimplifying something?

 

[Demystifier]

You correctly explained why gravity is dominant at cosmological scales, but the hierarchy problem is not about the cosmological scales. It's about values of various constants (or running constants) in the action, like masses and coupling constants.

 

[Roberto Pavani]

the hierarchy problem is not about the cosmological scales.

You're right, I misused the term 'hierarchy problem', that's about the coupling constants in the action, not about cosmological dominance.
Thanks for the clarification. My point was limited to the observational fact: gravity dominates at large scales simply because of charge neutrality, not because of the relative strength of the constants.