If that were true then states would not need the approval of Congress before being admitted, since the original 13 did not. They would just vote to ratify the Constitution, send their delegates to Congress, and carry on from there. But that is not what happens, is it? Congressional approval is needed for admission. The Constitution requires it. And when the original 13 states ratified the Constitution they agreed to abide by it's restrictions. And that includes Congressional approval for changes in their status, either by combining with another state or changing their borders by a fraction of an inch or, by implication, leaving altogether. In that all 50 states ARE on an equal footing.
It's really quite simple. One set of states entered unilaterally. Another group via acceptance by their soon-to-be peers. Once admitted, ALL the states possessed the rights of the ORIGINAL states - the Constitution does not divest the original of any powers, in fact the original members ensured that the federal agreement could not deprive them of said powers.
The US Supreme Court has repeatedly stated, '[u]pon the admission of a state it becomes entitled to and possesses all the rights of dominion and sovereignty which belonged to the original states', not vice versa.
The States are not the Suitors of Penelope that you make them out to be, trapped in a locked room with their executioner.
There is no "implication". The States are free to leave the Union, or to abolish it -- just as they made it.