They already did. It's called the 14th Amendment. SCOTUS has just been reluctant to declare its meaning binding until each enumerated right is reviewed individually.
You are corect.
In Binghams actual words...
CONG. GLOBE, 37th Cong., 2d Sess. 1639 (1862). Bingham states that among the privileges and immunities protected by Article IV, Section 2 were the rights to freedom of speech, press, conscience, assembly, trial by jury, and the right to bear arms.
Speech of Hon. John A. Bingham at Belpre, Ohio, September 14, 1871, supra note 70
John Bingham in the United States House on March 9, 1866 (Cong. Globe, 39th, 1st Sess., 1291 (1866))
On January 25, 1866, two years before the adoption of the
Fourteenth Amendment, Bingham made clear his belief that
the federal government should be empowered to enforce the
Bill of Rights against the states. Bingham spoke in general
terms about what was to become the Fourteenth Amendment,
then pending before the Joint Committee on Reconstruction.
He said it was a [Page 72] “general”
amendment which would give Congress the express power to
enforce “the rights which were guarantied [sic] ...
from the beginning, but which guarantee has unhappily
been disregarded by more than one State of this
Union, ... simply because of a want of power in Congress to
enforce that guarantee.”
CONG. GLOBE, 39th Cong., 1st Sess. 429 (Jan. 25, 1866).
(I can’t post the exact link but the CONG. GLOBE can be veiwed here.)
It's called judicial activism.