Earlier quoted context omitted.
I had responded to msla's comment about "typewriters and cheap printing presses". Those didn't exist in the 1500s. þ's disappearance from English is not due to either, though the lack of þ in available type faces was certainly an issue.
But the reference to "cheap printing presses" has to be interpreted as actually being a reference to type, as you have already done with your archive.org link. The press itself cannot either support or fail to support any graphical forms; there's no difference in the press whether you're using type or block printing. Press quality issues are things like "are the surfaces flat" / "how much pressure can the press apply…
I do get your point, but I think it's still wrong to use "cheap" to refer to the typefaces available for the Caxton and KJV Bibles. I suspect they were quite expensive.
The physical press is only part of the printing cost. The Linotype typesetting machine made it possible to set an entire line of type, drawing from a 90 or so characters. While the press itself didn't care, adding new symbols required manual effort, making it more expensive.