Are you saying we should somehow all go back to cash and also use cash online?
As for why you involved them, that is the actual issue at hand, because it's a choice, not something that was forced upon you. But the choice isn't the first one that comes to mind; the choice was between protecting consumers or protecting corporations. And in the US, corporations are better protected than consumers. To level that protection, you (a consumer) have to involve someone else (a corporation) to gain any practical protection.
If that method of protection wasn't needed, you'd be paying using a cheaper (or free) method where you'd be protected differently (i.e. not based on the money going from A to B, but based on the fact that you are a consumer and should thus be protected).
You could also go back to the first choice that might come to mind: protection. If you are not in a society that protects consumers directly, but you also don't want to pay a corporate provider for that protection, you could opt to forgo that protection.
And I think this means there is opportunity for disruption.
If they don't trust you enough to give you credit without a guarantor like Visa or Mastercard, then I don't think there is any way for you to force them.
There are businesses who let you purchase stuff online by bank wire.
Because you paid with a VISA card instead of paying by cash. Hint: it says Visa on the card.