Debt free vs Depreciating dollars when cash flowing

[Brian Naumann]

During my education process I've heard of two opposing points of view in regards to debt service when cash flowing rentals; 

Point One - Pay off debt as fast as possible. The theories I have heard are paying down debt with the profits to the point where your profits might reflect a $1 a month profit. Short term it seems like a grind and reduces capital that could be used for additional investments or owner's profits.

Point Two - Pay normal payments over the life of the mortgage. The theories I hear regarding this one is that over time the dollar (or whichever currency you use) is worth less and less. So in theory what might seem like a huge payment in today's dollars might be equivalent to pocket change or a cup of coffee in a decade or two due to inflation. (Think about Robert Kiyosaki paying a dime for comic books in the 50s that today run about $6-7)

I'm curious to people's opinion on this. 

Please, if you respond to this post respect everyone's opinions that also responds on this topic. I don't think there is a "right" answer so nobody can be wrong.

[Christopher Renda]

I don't have much practical knowledge here. But from I've been gleaning from Bigger Pockets and other books I've been reading and podcast I've been hearing, I'd say Point Two is stronger.
Nothing wrong with Point One. Seeing that after the properties are paid. Your cash flow will increase and you have lots of equity.
However, I see Point Two being a more dominant strategy. Because even if a housing market declines, for the most part, rental markets remain pretty steady or continue to increase. Also, the write offs you get from the depreciation and interest paid are noteworthy to an investor. So it's not just about having more capital to use on the next property.

I'll wait to read what those that have more actual experience doing this say. But that's what I've been learning thus far. YMMV