People love to bring up accessibility whenever cars vs. [any other form of transit] come up, because it's a convincing argument on the same level as "somebody please think of the children." Because of course the only way grannie can get to Third Beach is by car, straight from her doorstep to the bottom of the stairs. And the only way that can ever be possible is if we build a four lane road to handle them all, and add another acre of parking to fit all those extra cars that appeared for some reason. (See also: Granville Island).
I'm being facetious, but it is a hilariously popular argument. There are very good reasons to have a functioning road there, but while we're talking about accessibility, cramming bikes and pedestrians together on that section of the seawall is not it, and I'd argue it is a more serious accessibility issue than the road being congested. It was nice having that separation.
And alas, those other trails through the park are lovely, but they aren't very comfortable or efficient on a road bike.