Every actor dreams of their first big break, of course, but the four of them acknowledged that their individual ST roles were not crucial to the success of the show. And yet, ironically, they spent the most time with the fans in the 70s and 80s.
But what were they to do? In the 70s and early 80s, TOS was a huge success in reruns, and that can make it extremely hard to be seen as another character on the opposite channel. To turn down paid convention appearances in the hope of nabbing that new, big TV or stage role is another gamble, especially when their TOS contracts paid them royalties for only "one play and two repeats", and then the show was repeated ad infinitum, something unheard of at the time. (This also affected the cast of "Batman", IIRC.) These days, actor contracts have perpetual royalty clauses built in, to help take account of possible syndication longevity with may then threaten an actor's chance of new work (that would be in competition with older work).
If you don't believe in typecasting then you simply haven't met enough hungry actors.