The original colonies and states along with the writers of the Constitution probably intended that states would be so independent that there would be no point in succeeding. The problem is now, and always has been that we not only freedom to do what we want, but we also want to be able to force other people to act the way we think they should.
The original intent of the Declaration of Independence was to create a group of essentially independent nations with their own local self governments. The "united" part was intended to ensure that the small governments would have a framework to work together under an agreed set of minimum rights all the local governments would have to offer their citizens. The constitution even clearly sets out to state that the federal government is to have limits on it's own authority so that it can't give itself any additional power. That all ended when the united states went to war with itself.
Slavery was evil, I hope we all agree, but saying "no slaves in the US" doesn't work unless you also have the "and the southern states have to stay part of the US" clause. It's not even about equality. Lincoln was fighting to end slavery in all the US, and was willing to concede pretty much everything else to achieve that goal.
I will say then that I am not, nor ever have been, in favor of bringing about in any way the social and political equality of the white and black races — that I am not, nor ever have been, in favor of making voters or jurors of negroes, nor of qualifying them to hold office, nor to intermarry with white people; and I will say in addition to this that there is a physical difference between the white and black races which I believe will forever forbid the two races living together on terms of social and political equality. And inasmuch as they cannot so live, while they do remain together there must be the position of superior and inferior, and I as much as any other man am in favor of having the superior position assigned to the white race. - Abraham Lincoln
When Lincoln won a war to prevent states from having the right to separate from the union, the inescapable conclusion is that the federal government has taken, by immortal "might makes right," more authority than was intended by the writers of the formulative documents that created the united states. A lot of things changed at that point, but perhaps most relevant is that the US changed from being a group of nations bound together in mutual support to being one nation with all final authority bound into a single central government.
Much that is good has come from that change, and I think most of the citizens of the US have benefited from it. However, make no mistake, this is not the nation created by the Declaration of Independence and by the Constitution. This is a different thing. While those documents are of historical and interpretative import, they are not what make the United States what it is now as a nation.
Perhaps we need a new pledge. "We the people of the nation of America ('cause mentioning states is like mentioning city councils now and Mexico and Canada already have other names) have decided that we are one nation, no matter how divided in desires and opinions, independent of the authority of other countries, except the UN, for now, but completely at the mercy of one single federal government so that we can ensure our neighbors thousands of miles away have to do what we say, until such time as they can win an important election and then we'll throw tantrums and rise up to assert our independence. At least until the military style police organization we created to enforce our will on others comes to squash our own attempts at independence."
That seems a bit too long and complicated. How about something shorter that means the same thing. "The United States died a long time ago, and while fondly remembered, shall not be confused with our current nation. Long live 'Murica!"
The people of this nation are mostly good people. The government is mostly good. Being able to change our leadership without a war is good. I'm just having a tiny bit more difficulty stamping down my internal cynic this morning than usual.