Pretty sure that taking over the country would disqualify Speedwagon from its good guy image. Not to mention be something that would cause the Joestar family to turn against it pretty quickly since they hold to being good guys too. The part about having military assets can be explained by Speedwagon being a big part of the American governments magical powerbase and research and therefore extremely important aid when magical "problems" pop up(aka vampires, rogue magi who aren't working for the government or work for other organizations like the Clocktower, overly zealous or crazy priests, mystical creatures, and basically anything that would get in the way of the governments own agenda's when it comes to magic but wouldn't be too morally grey* for Speedwagon to complain).
*Such as the Grail War in Fate Strange Fake which the government created and started(they had agents in japan during the Third War and managed to get ahold of a fair bit of the Grails Workings, enough to make their own though they didn't have a Saber class).