Why I-keiyoushi is used more in reduplicated words than na-keiyoushi?
The usages of those "reduplicated words" vary.
- 仰々しい, 苦々しい, 馬鹿馬鹿しい: works only as an i-adjective
- 高々, 渋々, 延々, 脈々, 飄々, 黙々, 泣く泣く, ワンワン, ピューピュー, じゃんじゃん: works only as a standalone adverb (some are followed by と)
- 様々: works only as a na-adjective
- 直々: works only as a no-adjective
- 喧々諤々, 明々白々: works both as a na-adjective and a no-adjective
- 色々: works both as a na-adjective and a standalone adverb
- ピカピカ, バリバリ: works both as a no-adjective and a standalone adverb
- 軽々(しい): works both as an i-adjective and a standalone adverb
- 楽々: works as a na-adjective, a no-adjective and a standalone adverb
Note that adjectives can of course conjugate into their adverbial form and be used adverbially, too (eg 仰々しく, 様々に, 直々に).
Among these, probably the largest category is "only as a standalone adverb", because most onomatopoeia and mimetic words fall into this category. As you can see, even many kanji reduplicated words refuse to accept all of しい, な and の (we don't say ×飄々しい, ×飄々な, ×飄々の).
To answer your question, I'm not sure which is statistically larger in number. Is it really the fact backed up by some existing research? If reduplicated na-adjectives are really relatively less common than reduplicated i-adjectives, that's probably because many words are used as no-adjectives instead of na-adjectives.