Why armored cruisers barely joined the Great White Fleet

Why are the armored cruisers picked up on the West Coast not treated as part of the Great White Fleet?

They joined too briefly to complete a full leg, missing an opportunity to use their greater port access as part of the fleet's wider diplomatic display.

The cruisers appeared for only a limited part of the journey rather than completing even one full leg with the battleships. Their brief attachment therefore did not amount to sustained participation in the Great White Fleet's global demonstration. The later Empire Cruise provides the contrast: its cruisers followed the broad route but could detach for ports and waters less accessible to the capital ships. Contemporary armored cruisers could rival some battleships in size while generally drawing slightly less water. Their shallower draft opened more ports to them, making deployment choice part of their diplomatic value.