Actually, it's more the other way around: (reconstructed) Old Celtic looks quite like Latin to me—there's lots of elements I can recognise in names like Cunobelinus (hound of Belinus, cf. Latin canis) or Dumnorix (cf. rix with Latin rex, "king"); but when I look at modern Celtic languages, I can rarely make head or tail of them.

(As for Ogham, I get the impression that the orthography used in Ogham lagged several centuries behind the spoken languages, in much the way that written present-day English represents (in features like "gh" in "brought"—or "ea" in "features"); and that when people started using the Latin alphabet in preference to Ogham, the orthography leapt forward several centuries as a result.)