One Simple Reason Why Wizards Will Never Dominate Muggles (Sorry, Grindelwald)
The idea of wizards' superiority has always been present in the magical community. Not everyone believed in it, but still, if at different levels, most wizards considered Muggles to be lower than themselves.
There's a reason why every second wizard felt obliged to condemn Mr. Weasley's admiration for Muggles.
That's why Grindelwald's ideas were so popular back in the day: he claimed that wizards were to prevail and rule over Muggles "for the greater good".
The thing is, he completely ignored some objective facts — and so did every other wizard who agreed with his ideas in the slightest.
And there were extremely valid reasons for the wizarding world to remain in the hiding: primarily because the magic society was — and is — extremely dependent on the Muggle society economically.
Wizards don't do mining — where do their gold, silver, bronze, and steel come from? Muggles.
Wizards don't do agriculture — where do they get their metric tons of meat, vegetables, and seeds? Muggles.
But wizards also don't seem to directly trade with Muggles, you may argue — and you'll be absolutely correct. Guess who does, then? Goblins!
We can easily deduct that from the fact that Hermione's parents exchange their Muggle money for the "proper" wizard currency in Gringotts.
The only reason the goblins would be interested in purchasing Muggle money is if they did business with Muggles — otherwise, there would've been no point for them to set up an exchange in the first place.
But they need Muggle money to deal with Muggles. Also, they likely play on the market, because simple exchange services can't possibly give them enough Muggle currency for doing proper business.
What business could they have with Muggles? All of it.
In the magical society of aristocratic hoarders that pile up their gold in massive vaults to sit on it, there still needs to be circulation.
To ensure that, Gringotts buys gold from Muggles (remember, conjured metals don't last long and even then they can only be produced by Leprechauns) and issues new coins into the magical world.
It's no proper circulation, mind you, so there's definitely constant inflation of galleon, but we'll skip that part for now.
The goblins are also likely the ones who buy raw materials from Muggles to resell to wizards — to shops, to the Ministry, to Hogwarts…
Everyone needs something to eat, and food is one of the five exceptions to Gamp's Law of Elemental Transfiguration. It can't be summoned, and goblins are surely quite happy with that.
There's an infinite number of other things wizards don't bother to produce but consume on a daily basis.
This creates an interesting scheme where the wizarding world is completely dependent on Muggles — but since the wizards themselves don't realize it, goblins take full advantage of it, hence making wizards dependent on them, too.
Wizards revealing themselves to Muggles or trying to overtake them would most likely result in a massive war.
It would completely cut off the supply of the most crucial items for the wizards, effectively dooming both their economy and society. So the safest choice is staying safely away, ripping the fruits of Muggle's labor.