Certainly many people purchased the Fire because it was a inexpensive tablet but many chose the Amazon Ecosytem because they were perhaps already embedded. While there are other e-readers at a cheaper price, they wanted a tablet. This in spite of the fact that they could have purchased a better equipped iPad for just a $100 more. Not unreachable if you are patient and really wanted it.
The Fire was successfull as much for it's Brand Name as it was for its form factor. There are other similarly priced Android Tablets as the Fire, but the Amazon Brand was the distinguishing difference.
The iPad has many competitors on specs and price points yet it dominates for many reasons, but the main reason is the Apple Brand/Ecosystem. Why would a choice for the Amazon Fire be based on different reason? Does Amazon not maintain customer loyalty? Ask Borders that question.
I agree that most Fire purchases are based on brand name and the association with Amazon. Especially with older users who just want to keep reading books but see a value in going digital, they want to "stay with Amazon" (although that fact makes me want to slap them), and just get a good eReader. These people are unlikely to want or be in the market for anything more than an eReader and would not normally buy the iPad anyway.
However I think you are making a couple of assumptions here that are simply not in evidence. First, there is really no evidence at all the the Fire is "successful" and sells in anything like reasonable numbers. There is on the other hand much anecdotal evidence that it's a very unsuccessful product and that customer experience with it is awful and that the return rates are high. Amazon purposely never releases sales figures in order to mask situations like this. Without the facts, perception is king, and while the perception is that the Fire is a "competitor" and "does well" this is in fact pure speculation from reviewers operating completely in the dark.
Secondly, You are assuming that the Fire is a better, more popular choice than the basic Kindle, for which all the arguments you make for the Fire can also be made. Again, facts are few and far between but the information that has leaked out so far would seem to indicate that the original Kindles do better than the Fire's and are more popular overall.
The Fire 2.0 might do better, but literally all actual evidence on the matter shows the 1.0 version to be a slow, clunky, hard to use, error-prone POS that doesn't actually sell well at all and hasn't cannibalised any markets or put any competing products on the ropes etc. It's to Amazon's credit that they can work the propaganda machine to the point that most people actually believe the exact opposite of this, because it isn't really true at all.