I see no reason for it. The thu'um powers are supposed based on stealing dragon's souls, directly absorbing their knowledge. Not by leveling other skills. There isn't supposed to be any education involved.
Actually, the Thu'um is a power that usually requires heavy study and experience with to become powerful with it. Every Nord has the ability to use the Thu'um, but only a handful have studied it. The thing about the Dovahkin, is that he can absorb such knowledge//experience from Dragons when he slays them, because he has the soul of a Dragon. That's what makes the Dragonborn so special.
It'd be pretty cool if the right hand side of the "Speech" tree was perks that buffed Dragon Shouts, instead of some [censored] "Bribe/Persuasion/Intimidate" perks, especially considering those options don't pop up enough in dialogue to be worth it, and just raw skillpoints in Speech are more than enough to succeed at such checks. Have a perk reduce the cooldown of Shouts by 20%, and another perk increase the duration/potency of shouts by 25%, and another perk that increases the range/AoE of applicable shouts, etc.