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But they were able to setup the core of their commercial and governance infrastructure in the middle of London, with no particular notice from muggles - not to mention, we know that the government already knows about wizards (MoM liaises with the PM). So there must be a quid pro quo already in place, with the government tolerating and aiding in the existence of a semi-independent polity in their heartlands in return for unspecified benefits, probably defence against foreign wizards.
But the inverse also applies - there’s not much stopping wizards from portkeying/apparating into the Oval Office or the pentagon and magibombing them, or Avada-ing key targets. Wizards are probably the worst kind of guerrilla fighters - ones unchecked by range. And as far as food is concerned, food multiplication is a thing. I personally believe that in the long term, the way muggles would win would be through subverting wizards, not by pure overwhelming force.