The founding fathers and many others would disagree. Based on human history, your assessment of the average human's level of integrity and reasoning is irrationally optimistic.

Also, I assume you meant to say "Direct democracy is a representative democracy where each person *is* a representative."

It doesn't matter because everyone only has to represent themselves so they don't really need to have integrity or ability to reason in some larger sense, they just have to be selfish — which is a lot easier than reasoning your way to what maximizes societal good, or some average of the opinions of the 100'000+ people you are supposedly representing.

And the amount of power an individual has is negligible so a bad vote is diluted much more than it is in a representative democracy.

You realize that a certain "institution" would have died out much slower (if at all) in the US if what you said was accurate?

I think that's the only example needed to prove that direct democracy is not a desirable form of government, let alone the ideal.