You just defeated your own argument here. The nail in the coffin as it were. Since you admit that Congress already had the right of funding the militias and passing laws regarding their organization and training, then why pass the second amendment? To restate what Article I, Section 8 stated?
You walked dead into this little trap you set for yourself.
Since the Constitution, before the second amendment, already established Congress as being responsible for "organizing, arming, and disciplining, the militia", the need to provide in an amendment for "a well regulated militia" is moot.
A well regulated militia was already established by Article I, Section 8. Since that portion of the Amendment was a given, it is only the second section that provides new protection. That is, the rights of the people to keep and bear arms shall not be infringed.
That WAS the reason.
The U.S. Constitution gave Congress the power to arm the state Militias. The question arose, "What if Congres refuses?"
Since the power was concurrent, the states themselves could arm their Militia. The second amendment protected their ability to do so.