I would at this point in time, like to point out that the No trail of tears achievement in EU3 is staggeringly easy if you just abuse how dumb the AI is. Personally once I discovered it's weakness and used it to ruin their chances of colonizing NA while westernizing, I was able to create a massive westernized NA colonial nation that made every single European power look feeble.
My point here is, the AI doesn't stand a chance vs European powers, but you as the player do. Let's just be honest, unless the AI is programmed to westernize asap it will die and anything else would be silly. I'm not saying it should be no effort, it should be costly and so forth but it isn't the individual arms that make it hard.
What makes it hard is the cost and attrition of sending troops and if you are defeated by the natives then it should be through vastly superiour numbers. That will make it as it was.
The player character will still be able to exploit AI weaknesses and pre-knowledge of history (remember, they didn't know about Europe, you do! You will spend hundreds of years preparing for this EXACT scenario).
So you can make yourself an american superpower as a native power...if you're a masochist, sure, it'll be possible. But the natives are not going to defeat European powers, oh they might push back a stupid and poorly planned force, but they're not going to be in this for the long haul.
Look at China in EU3, big, mighty, organiced and yet...I don't know about you guys, but I've amused myself plenty of times slaughtering hundreds of thousands of their poorly equipped troops with my colonial forces. Which may sound imbalanced but does tend to mirror reality as well.
The american powers have nothing on china, china blows them out of the water, yet china itself in EU3 must see itself a victim to European aggression.
Let's just face it guys, for the last thousand years we (the Europeans and those of European ancestry among us, yes Americans you count as well, you're a colony not a real country) were damn good at butchering, conquering and submitting our fellow human beings.
There were a lot of things we failed miserably at but during the period of this game Europe was a steamroller of total helldeath and if this game is to remain even remotely accurate then it just will not be balanced across the globe.
The only realistic challenger to Europe in this period were the Muslims in the middle east, north africa and Turkey. Any other nations had the single advantage of geography, which can indeed be a powerful ally but isn't going to cut it when the troops are finally lined up.