What is the benefit and purpose of reading lots of books for your pet? does a pet magically or intelligently get stronger during battle?
It won't make your pet stronger, but at certain levels your pet can use special effects of certain items such as: Short Sleeved Yellow Tunic Crisp Blue Tunic White Linen Tunic Tunic of Warding Heavy Robe Of Thievery
Battledome wise, I guess what Commy mentioned above already gave you insight. But aside from that I do believe that people who have their pets reads a lot of books probably want the book trophy. That's pretty much all you get I suppose. Not to mention there are very HTS books out there and usually people who read books have advantage since they might be able to get it for a big discount.
The only reasons why I would read books to my pet are in order to use certain BD items, or just if I got bored. It's just another goal to set. It's like neohomes and stuff...they don't really do anything, but people make them anyway. It just depends on what your itnerests are and such.
It all depends what you want to do. Out of the BD weapons, only the CBT and the HRoT are any good, and with the HRoT you need a really high agility as well. And while it is a 100% stealers, stealers aren't very high on a BD set. There are a lot of things to get, that can cost tens of millions before you would want to get a HRoT. And as for attempting to get the book trophy, it will also end up costing millions. Aside for the aesthetic value of having a pet with decent intelligence, there isn't much use for it.
I do it because it's really irritating to have awesome battledome stats and then just underneath a line saying my pet is a dunce xD