It is NOT a powerful argument. You may need to improve your reading skills.
Your “most precious right” follows Life and Liberty and is endowed by a Creator. The Declaration of Independence is expostulating reasons for government’s existence, not granting you rights.
If you think government should go beyond the scope of the US Constitution to make you happy, feel free to start your own revolution.
From the declaration...
“We hold these Truths to be self-evident, that all Men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the Pursuit of Happiness.
Here’s a helpful hint - it’s important you pay attention when you read something.