Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes;
The reason I stopped short is because that next section adds nothing to the point. "Should not" is a suggestion, not a requirement.
Furthermore, your point ignores the fact that the Southern States did not consider their independence movement to be a consequence of "light and transient causes." They considered the issues separating the North and South to be quite serious and intractable.
Like other associations, the freedom to join doesn't necessarily mean you can justifiably leave anytime you want.
Associations like the Mafia perhaps, but I know of no legitimate association that says they will kill you if you try to leave.
Why, then, should the D of I have not simply been a one-liner announcing that fact? You explain away all the D of I except what suits you with "'should not" is a suggestion, not a requirement." We've already been over that - the D of I is not mandatory legal authority but rather persuasive authority and yet the D of I does state some requirements for secession already mentioned.
Here's one I haven't yet mentioned:
a decent respect to the opinions of mankind requires that they should declare the causes which impel them to separation.
The rest of the D of I, which you summarily reject, explains and shows what a declaration of session should look like, including what are NOT "light and transient causes".
Of course, there's a problem with your rather simplistic free-to-come-free-to-go premise about formal associations. When you as a principal freely join or form a corporation or a partnership with others, mutual trust is formed, mutual benefits are conferred, and you and the others generally have skin in the game. And it is generally contractual. You don't just "back out" of a contract simply because you freely entered into it. Usually you cannot just "leave" a formal association or break a contract just because you decide to without a penalty because others who have relied on your association are now suffering detrimental consequences from your decision. Marriage is probably the easiest example. Associations in the business world like partnerships and corporations are another example.
Usually, a good business association includes agreements on how disassociations will work. Usually you have to have a good reason for leaving and if not, you may have to pay some kind of penalty. The point is your simplistic scenario of freedom to leave without consequences, is not how formal, contractual associations, including political associations, work out in real life.
In this case, the Constitution itself was tailored and ten amendments added to accommodate all potential ratifying states. Those that hated slavery held their nose and allowed it in the Constitution believing that the Union was the most important thing and that slavery would naturally die out, which it would have I think. And there is a legitimate argument that statehood is a contractual agreement with the Union and one that can't simply be broken without certain steps having been taken.
The D of I is persuasive authority about what it takes to legitimately disassociate or secede from a government. Your premise denies the need for a D of I that explains session to the world, only possibly an announcement of secession. I and our Founders would disagree with you. Not sure what else there is to talk about.