Right but there's P AND I and P OR I. One is Article IV Section 2, the other is a clause of the 14th amendment.
I haven't seen or heard anything that states the 14th amendment clause was a replacement for Article 4 section 2. And that would conflict with contemporaneous rulings of the era which held the clause was specifically designed to deal with freedmen after abolition. Especially in the Slaughterhouse Cases that somehow (I'm still not clear on how) removed a lot of the teeth from the clause.
With that stipulated, it could be argued, and probably somewhat effectively so by someone more talented and knowledgeable with the law than I, that as the two are distinct, the Slaughterhouse Cases don't apply to Article IV Section 2, because the rulings in Slaughterhouse touched on the scope and intent of the 14th Amendment very heavily.
So if we instead rely on Article 4, we can minimize the effect of the Slaughterhouse Cases- and argue we're discussing the Privileges and Immunities of all citizens not the narrowly defined and held subset the Slaughterhouse Cases limited the 14th Amendment to.
They are sufficiently similar to serve our purpose, without the baggage.