
David J. answered 09/19/20
Highly experienced and effective PhD organic chemistry tutor
Firstly, I would question the premise that free radicals don't undergo rearrangement.
Second, one must appreciate that free radicals are electronically neutral species, despite being octet-deficient and thus highly reactive. The reason a secondary carbocation rearranges to a tertiary is because the additional C-group, which is electron-releasing, inductively stabilizes the positive charge through the sigma bonding framework.
For neutral radicals, there is no such advantage or mechanism.