I’m playing with the idea that regibus regna reddere might have sounded Ennian to Cicero’s audience or that he might have been inspired for the alliterative turn of phrase from his exposure to Ennius. Just speculative, but here are some supporting details:
When commenting on Aeneid 3.333 (…regnorum reddita…) Servius is reminded at least by the verb of Ennius:
more veteri pro ‘data’ accipiendum est: ‘re’ ergo abundat. Ennius annalibus “ad illa reddita nuptam”, et alibi “isque dies post aut Marcus quam regna recepit” pro accepit. aut ‘reddita’, quod Heleno debebatur imperium.
Skutsch on his commentary on F.56 of Ennius’ Annales does not believe that there is anything particularly archaic about this use of reddere.
Statius uses the phrase reddere regna to start THREE different lines in his Thebiad (2.541, 7.390, 10.583). Book 7 in particular is known for having Ennian echoes.
Among the fragments of Ennius we find:
mortalem summum Fortuna repente
Reddidit †summo regno famul †ut †optimus esset (Ann. 312-313)
parentes vinculis exemisse, patri regnum reddidisse atque ita in (Euhem. 90)
And, of course, alliteration is often associated with Ennius…