Comment by elashri

Dirac was not working in vaccum . Klein-Jordan equation was the simplest and the most obvious extension of Schrodinger equation in relativistic manner.

So historically, Dirac was focused on correcting the Klein-Gordon equation, which had issues with negative probabilities and describing electron behavior. His goal was to find a relativistic equation that resolved these problems while maintaining consistency with his own matrix mechanics formulation of quantum mechanics.

By extending his matrix mechanics formalism, Dirac derived an equation that not only addressed the issues with the Klein-Gordon equation but also predicted the existence of antimatter. I would argue that Dirac's approach was consistent with his established framework, and while he found renormalization mathematically unsatisfactory, it does not diminish the validity of his method in deriving the Dirac equation. I doubt he focused on any elegant solutions, he was actually quite happy working with matrix mechanics framework.