Are the bedlam quests bugged

If the quest doesn't provide an outright reward, are you sure none of the following are true?

• Did the quest pave the way for another quest?
• Does the quest-giver NPC like you enough now to follow you or marry you (disposition raised)?
• Fun loot somewhere in the quest-related area?
• If NPCs died, did they drop any keys to doors or buildings?

Some quests are just there to be tasks, not all have awesome rewards. Some might be tutorial-like quests (especially if you got it in a town).

Also keep in mind that there are two quest-related achievements beyond the main quest and faction-related achievements:

• Sideways: Complete 10 side quests
• Hero of the People: Complete 50 miscellaneous objectives

Throw Voice is unique in that there's no benefit to a higher magnitude power of the effect. The enemies are distracted, and investigating somewhere, or they simply aren't. It's a binary either/or scenario.

So, Bethesda had to find some other benefit to the 2nd and 3rd words - there was no magnitude or duration to increase like most other shouts. Their response? Lower the cooldown.

So while there's never any reason not to use the level 3 shout, it still requires 3 dragon souls to reach that point, and given that you learn all 3 words of the shout simultaneously (unique among non-unlocked shouts like Dragonrend or Clear Skies), it's not inconceivable that you may need to go dragon hunting before you can use the level 3 shout.

So to definitively answer your question: no. In all likelyhood, the recharge times are in the correct order, even though this is relatively unique among the shouts. (For another example, see Call of Valor, which has identical recharge times throughout all 3 levels).