Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons. Isospin symmetry remains an important concept in particle physics. A close examination of this symmetry, historically, led directly to the discovery and understanding of quarks and of the development of Yang–Mills theory.
As modeling developed into the quark model, with the table of quarks as seen in the standard model of physics, the isospin became the quantum number characterizing the quarks as seen in protons and neutrons, to separate the strangeness and charm couple (generation) , and the top and bottom couple. Analogously one might say "upness" and "downness". The algebra is the SU(2) group algebra when building up the isospin of hadrons.
Up and down quarks each have isospin I = 1⁄2, and isospin 3-components (I3) of 1⁄2 and − 1⁄2 respectively. All other quarks have I = 0. In general
Would it be more correct to say that isospin comes from quarks rather than nucleons
Yes, keeping in mind that in particular it defines up and down quarks only.
In particle physics it is not a very useful concept, other than in separating up from down quarks. (The rest of the quarks have individual names instead of a spin type representation). This answer of mine to a different questions is related