A Concertmaster is a violinist because they’re in a front-and-center leadership role within the orchestra. The violin section is generally the largest section of the orchestra, with its members playing throughout the majority of a performance. Since the Concertmaster is the leader of this section and will make all decisions about the section’s bowings, it only makes sense that they’re a violinist.
In their role as a liaison with the Conductor, the first violin’s physical proximity to the Conductor’s podium also makes sense.