"The Menagerie" doesn't impress with its dramatic values. "The Cage" is a story that deserved to be aired, even if in this somewhat truncated form - but the framing story is a senseless collection of unconvincing transitions and implausible actions, and the extremely thin story there only serves to undermine everything "The Cage" stood for.
I think that Cpt. Pike's drive for freedom in "The Cage" is not incompatable with going to Talos 4 in the end of "The Menagerie" because he's in an even worse "cage" now, his own body. So a healthy robust Pike wouldn't want to be trapped in illusion, but he is neither and his imprisonment even more oppressive. I understand his choice.
But, this leads to another problem, why doesn't the Federation negotiate with the Talosians to open a hospice on their planet for similarly disabled citizens.