Well, how would the declaration apply today? Are we the subject of a despot? Are we not given representation in our government? Has this despot made our representatives go to "places unusual, uncomfortable, and distant from the depository of their Public Records, for the sole purpose of fatiguing them into compliance with his measures"? Is the judiciary subject to this despot's will? (and so on...)
Since you intentionally skip many times answering my question how it was applied in the past and when the application was ended, I have full reason to believe that you try to escape from facing the question that you proposed: "The Declaration has no application today". On the contrary, I am able to answer your question regarding the past and present application.
An absolute fundamental application of the Declaration is her function and application to make the Constitution valid, and the validity of the Constitution must depend on the Declaration forever. Once the Constitution is allowed to isolate from the Declaration, the constitution is no longer the same thing that the founding fathers intend it to be.
Second, you cannot imagine that the removal of the Declaration can leave the Constitution to survive the grasp of some despots. This topic can be quite involved, I'll leave it for your understanding and imagination. However, if you insist me to furnish you with some thorough explanation, I will not hesitate to do that. I will not escape. But, at least, do you see how many amendments the Constitution has allowed herself to have? Without the principle guidance from the Declaration, some force can eventually make the Constitution gradually drift along some direction that another group of people do not agree. You can say that in a society, different groups of people always disagree with each other. But, if the Declaration is allowed to apply, one group of people can silence the other group with principle that both groups have accepted. Other wise, the silence will be realized through force, power, violence.
"Are we the subject of a despot?" The despot is in the formation; an embryo has been obvious. In fact, where did the founding fathers find the principle that forbade them from having a Constitution that was governed by a despot (but only so far)? The Declaration!
"Are we not given representation in our government?" Yes, we do; so did Soviet Union of Russia, so do Communist China, North Korea.
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Has this despot made our representatives go to "places unusual, uncomfortable, and distant from the depository of their Public Records, for the sole purpose of fatiguing them into compliance with his measures?"
When the Black Panther members waved the baseball bet at the voting station, I did feel uncomfortable to go there; but some of our representatives did make some other representative not to pursuit the case, even the law should have been against the panthers (oops, I forget them being human beings, sorry). Can I reach my hand to your pocket to get $10? You'll say "F*** off". However, someone has been able to force the government to reach deep in some working people's pocket for money to feed someone who does not work. The despot's meat grounding machine has not been able to fully operate yet; it is on the way.
"Is the judiciary subject to this despot's will?" What do you think of that a mosque is escorted to be erected with triumph next to the place we feel heartbroken? What do you think of that our border must be maintained fully opened for criminals' pleasure?