What if Amon and the Equalists had decided to set up shop in Ba Sing Sei first, instead of Republic City? There is clearly a more prominent divide between rich and poor there, in addition to an actively malicious government as opposed to a merely inept/indifferent one like RC has? Hell, even when things were at their worst under Tarrlok, he never disappeared people in the middle of the night for being inconvenient either. Additionally, the Dai Li wouldn't be much good against Amon's powers for the most part either, so there's less chance of him being abducted before the movement could get going...
...Though on the other hand it appears that a level of indoctrination is in place in the city, as shown by Mako and Bolin's grandma praising the Earth Queen's statue, so maybe RC was a better target as its comparitively liberal setting allowed him to set up shop easier? Like, I don't think that the Equalists could get away with protesters in Ba Sing Sei, for example.
Yea he'd likely never have gotten the sizable force nor backing if he'd started in Ba Sing Sei. Secret Police grabbing most his people and it being a much harder climb to convert them since the Bender non Bender divide doesn't seem to be as sharp as it is in Republic City. That an no body with the wealth to back him for a bigger movement there unlike Future Industries central location.
It is a wonder if there are places that don't seem so bender strong where he could have made a start.
Maybe the Fire Nation back in Ozai's time, as political power seemed to be at least partially tied to the ability to bend with only the archers and swordsman dude seemingly being the only people of prominence that couldn't.
Even in the latter case, apparently Sokka's master came from a noble family and was considered to be a disappointment for his lack of bending ability, hence what spured him on to becoming the Greatest Swordsman In The World in the first place.
But then, they had the same indoctrination issues that Ba Sing Sei now has, what with regimented schools, history altered to support propaganda (the "Air Nomad Army" from the Footloose episode, for example), so maybe that wouldn't work either.
Really it seems that Republic City is increasingly the only place that Amon and the Equalists could have started, what with the comparitive freedom of the public to start such a movement in the first place, combined with visible concerns that cause Amon's support to grow more.
It would depend upon how many non-benders were in high positions. If the Earth Queen and most of the ministers were non-benders then Amon wouldn't be able to claim that benders are oppressing non-benders.
Though Amon could claim that rich non-benders are using benders to oppress poor non-benders and try to get the poor to support him by weakening the Dai Li the Earth Queen would probably respond much more harshly than the RC Council.
I don't think that he was intentionally trying to live up to his father's legacy though, circumstances just lead him into the same kind of direction he'd have gone if he hadn't run away from home.