I don't think the show was ever intended to be a kid's show like "Commando Cody," but the fact of the matter is that I got hooked on TOS when I was seven or eight or so, and I suspect that many of us were also hooked on some generation of Trek at an impressionable age. And, honestly, I don't remember having any problem following the plots or being confused by the TOS-level technobabble. Even if you don't know the big words, you can usually pick it up from context:
The transporters are't working because of science-y stuff, but Spock can fix it by doing science-y stuff, if only Scotty can fix the "dilithium" thingies in time!