I really have a hard time understanding why some people always want to delete the U.S. Championship from consideration.

Let's look at this step by step:

2002Brock Lesnar takes the WWE Championship to Smackdown, so Raw GM Eric Bischoff creates the World Championship for Raw.  Both Championships are understood to be of the same value.
Still in '02WWE Tag team Champions Lance Storm and Christian jump from Smackdown to Raw, so  Smackdown GM .Stephanie McMahon sets up a tournament to crown Tag Team Champions for Smackdown.  Again, the gist is that both sets titles were to be viewed as equals.
2003In early June, Raw co-GM "Stone Cold" Steve Austin announces a Battle Royale to crown a winner for the newly reactivated Intercontinental Title, so then a couple of weeks later, Stephanie McMahon set up a tournament for the newly reactivated United States Title.  The timing of this was done purposely to show that the I-C and U.S. titles were to be viewed  as parallel to each other.

Even though Vince McMahon didn't come from the mountain top with stone tablets making a proclamation, all of these new titles were introduced in such a way as to show that they were the equals of the originals.

It's just a simple case of putting 2 + 2 together and figuring it out, not everything has to be spelled out for something to be understood.