Do you not find that you get lost in your thoughts about the "debate"
No, because if you are debating someone and they're sitting there you don't actually fade away into a dreamland. A good example of this is, take something you already know really well — like a hobby or a favorite public figure. When someone or some book starts clearly misrepresenting that, you often feel a tug in your gut and your vision zooms into the text with motivation to explain exactly how it's not correct.
So it's a conversational energy ('WHY do you think that? let's see why'), and not rumination style ('why do you think that? i will put down this book now and rage as i stare out the window and pretend like i'm not debating you anymore')
What you're probably picking up on is this: it can take practice. Any exciting mental style is liable to make you go off on tangents. But if the only alternative is to subtract that, that doesn't make sense instead of just learning to hone what feels right already in your favor.
How does this affect your concentration when reading?
I am seriously, no-joke, partially 'high' sometimes. I practice concentration meditation, and the words naturally turn into meditation objects. In other words, there are forms of non-boredom that are feedback loops in a good direction. Here is Buddhist monk, Georges Dreyfus, explaining his experience in the book 'The Sound of Two Hands Clapping: The Education of a Tibetan Buddhist Monk'——
Whereas previously I was unable to sustain study of even the topics that interested me, I gradually became able to concentrate on any topic. I thus realized that anything can become interesting, provided that one puts one's mind to it. Interest and boredom are largely functions of the quality of one's attention. An attentive mind is not bored, however trivial the task...
These important benefits are not unlike those provided by meditative training, which is even more effective in giving its practitioner the ability to be attentive and concentrate, as well as the experience of mental calm.