I'm trying to show the problem with such applications; but I don't know, maybe many in the church today have never been taught inductive Bible study and are actually fine with filtered interpretations. That is my actual concern...
In my experience, filtered interpretations are pretty common. People spot particular trigger-words that mean something to them (be it 'blood', 'grace', 'faith', 'salvation', 'justification' etc) and think "oh, I know what
that refers to". Thus a person's huge and complex understanding of one or more concepts can get read into a biblical passage just because a
single word is present in the passage. People are simply really really good at spotting their own theologies in the Bible because a single word can be interpreted a referring to an entire doctrine time and again. I like to think of it as wearing Eucharist-tinted glasses... they see the Eucharist (or whatever doctrine) in any passage they look at because they put it there. I had one amusing experience where I pointed a person to a passage due to it being 100% opposed to their theological beliefs, and then they responded by seizing on one particular word in the passage as an excuse to read their whole theology into the passage and then convinced themselves it taught what they believed.
Now I agree with you that this does not really make for good biblical analysis. I prefer a much more academic/scholarly approach to carefully interpreting biblical texts. However, it's something that's really hard to get away from - everyone is naturally inclined to see ideas that they are used to in a piece of text when reading it, and less naturally inclined to see ideas that they are unfamiliar with. Even influential theologians can be extremely prone to expanding single trigger-words into whole doctrines.
Getting away from the tendency to do this myself was a real struggle for me personally. As I studied the Bible carefully I began to increasingly question and reject as unbiblical the doctrines that I had grown up with. Yet for a long time my natural / intuitive reading of several passages was still in agreement with the views I had grown up with, because I had learned a certain way of reading passages which I struggled to leave behind. The net effect of this is that it's always incredibly hard to convince anyone to change their theology by citing the Bible, because people are so extremely good at reading their own theology into any biblical passage you care to name.
This is why I am always fascinated to see an entirely new reading of a biblical passage from a point of view I haven't seen before (like the Eucharist-centric reading here). Because I realise that people who come from different backgrounds to myself will naturally have ways of reading that I won't have thought of. And one of those ways of reading could potentially be what the original author meant, but if I haven't thought of it, I can't fairly assess that possibility.