You know, it's probably worth noting that we're talking about a spectrum when it comes to the audience's knowledge of Star Trek. At one end, you have people who don't know or care who the captain of the Enterprise is, and at other end, you have the lifelong fans who can quote chapter and verse on every episode. But those aren't the only options--or very representative of the general audience.
In between, you have millions of people who have enjoyed the occasional Trek movie or TV series over the years, and maybe even watched TOS or TNG semi-regularly, but whom, for whatever reasons, had gradually drifted away from the later spin-offs and movies. But whom, yes, still know who Spock is and what "beam me up" means.
Somewhere in the middle of that spectrum is where the vast majority of the audience lies, not out at either extreme. It's not an either/or situation pitting hardcore Trekkies against total newbies.
Rebooting TOS, but without forty years of baggage, was the smart, sensible way to reach that huge middle ground.