Haha...I don't think it is a caricature.
I started attending a church with a Reformed Baptist pastor, but the membership is not Reformed. He said the previous pastor was a KJV Only dispensationalist, and had a long timeline stretching all the way down a long hallway.
Concerning "literal approach to Scripture", I think you need to study how Jesus and the apostles used OT Scripture. Did they apply Scriptures pertaining to Israel to the Church, whether explicitly or implicitly?
For instance, does Peter call the Church a "kingdom of priests", and a prized possession, with an obvious allusion to Exodus 19, where it is talking about the Church?
By the way, I don't view their "literal approach" as being a good thing, nor do I view it as being a consistent application..because they themselves will recognize symbols and figurative speech when it doesn't conflict with their worldview. Yet they will level charges of "spiritualizing" or "allegorizing" when simple types and shadows/fulfillments are recognized by non-dispensationalists.
And, they commonly level charges of antiSemitism toward non-dispensationalists.
Let me give you an example, from Chosen Peoples Ministries..this guy deliberately tried to slam non-dispensationalists to a Jewish audience, and claims non-dispensationalists are anti-Semitic:
And this guy admits issues with their hermeneutics, in that types and shadows are valid:
Pay careful attention though..he claims believers are high priests and this is clearly false.