Why the need for TSP solvers when there are SAT solvers?

Concorde TSP is a solver for TSP. SAT solvers are solvers for boolean satisfiability. TSP and SAT are NP-complete.

Hence, why spent the time to develop Concorde TSP when there is an abundance of SAT solvers in the market back then?

When you reduce one NP-complete problem to another one, the size of the problem usually grows polynomially. For example, when you reduce a HAMPATH on a graph with $n$ nodes to SAT, the resulting formula has size of $\Theta(n^3)$ (I don't remember about the constant that arises in a straight-forward TSP->SAT reduction). If you use the Cook-Levin theorem, then the growth might be even bigger because a Turing machine might have really huge (polynomyal) overhead. NP-completeness is mostly a theoretical idea. So is a polynomial-time reduction. Many theoretical papers only state that there is a reduction, saying nothing about how practical it is.
Let's informally assume that TSP is as hard as SAT. It means that it takes similar computational resources to solve TSP on $n$ nodes and SAT with $n$ clauses if you use state-of-the-art solvers for each problem. Now it is easy to see that writing a separate solver is more practical than reducing the problem to SAT and using some existing SAT solver. It is all about polynomial overhead.