I pay less than $2 apiece for cotton caps, buy them from Nashbar's clearances (sometimes 4 for $7).
Currently have 4 in rotation. Washed after each ride, hang dried.
The looks and colors mean nothing to me, I'm not a model, I bike to bike and don't give a **** how I look in the process.

Wear them exclusively without a helmet as I use helmet only for mountainbiking.
Had a coolmax one, made by Headsweats, it lasted about 2 seasons (less than 6k road miles) and started falling apart. Cost me $15, was not worth it.

Make any fancy "bike hat (with lid)" as you call them, I won't buy any of yours. $2 is my top price I'd be willing to pay.