Tellarites only appeared in a single episode of Star Trek, really - "Journey to Babel". They were set dressing in all the others, except that "Bounty" portrayed a specific individual who may or may not have been representative of his species.
So we can't really argue that the Tellarite species would have been described as single-dimensional or multifaceted or anything in between. Their story simply hasn't been told yet.
Many novels lazily only address the "straightforward social code" of the species, but that's Trek novel writing for ya. However, immediately after TOS, the early RPGs and fan works created backstory for the Tellarites, for example establishing them as skilled and hard-working engineers (in the same average sense where Klingons are warriors and humans are explorers), sometimes also as mining specialists, and generally less interested in space travel than some other UFP species but pragmatically exploiting what little traveling they do to the hilt. In some ways, they were the Ferengi of the early years, too: a greedy, devious, loud-mouthed but still essentially white-hat Tellarite merchant was a typical character in fan fiction or RPG storylines.
ENT was the first show to return to the species in any depth. The refined makeup, especially regarding the hands, has made many suspect that there are several variants of Tellarite biology, and that ENT and late TOS were correct in showing a pure-blooded Tellarite with five digits, while the three-digited "Journey to Babel" pigs were actually hybrids of Tellarites and some other species... Others argue that the five-fingered individuals are the hybrids, having average Trek humanoids in their bloodline to promote that particular hand type. Only some early fan works, RPGs and computer games still bother to support the notion that Tellarites would have hooves for feet...
Timo Saloniemi