To me, it always seemed that continuity was never was barrier to the storytelling, and, if the Enterprise haters are to be believed, ENT continually broke continuity.
That was because continuity becomes a nuisance and yes, a barrier, to doing anything interesting so ignoring or destroying it is worth doing.
I know some people don't see that, but if one doesn't then one has the choice of either being offended by it (like some of the anti-Abrams nutcases) or shrugging and accepting it - because it will
be done by people who are actually trying to create good stuff and who therefore face the necessity. It will be done over and over, forever.