This is a great collection of questions, although they get a bit tangled together in different ways and they also show how a lot of the popular information available about linguistic history is not terribly accurate. I want to make a few general comments to give a little bit more context before I try to tackle a number of the individual questions.

At the time that the printing press was introduced to England during the 15th century, what would generally be recognized as the late medieval period, the idea of a standardized, written form of the English language didn't exist. There was no such thing as a complete dictionary of the English language, nor would there be for many, many years. There could be considerable variation in how words were spelled across multiple regions and times. For instance, the common, every-day word where could at various places and various times during what we would call the Middle English period (~1100-~1500) be spelled as where, hwere, were, whear, wheare, quer, quere, qwer, qwher, quheir, war, ȝwar, hware, whaire, quare, qwar, and quhar. And that doesn't even exhaust all the possible spellings listed in the Oxford English Dictionary. Individual scribes might develop particular tendencies, but even then, they might use several different spellings for the same word across a text. We are so trained to think about the "correct" spelling of a particular word, but that didn't exist for English at the time. A scribe could write bac, bak, bakk, or back, and none of them would have been any more or less correct than any other one. It's not that the possibilities were unlimited. No one scribe would have used all the variations of where listed above. But there were many fewer constraints. The history of English orthography (a fancy word for spelling) is all about tendencies that gradually develop into a kind of written standard over a period of many centuries, and often that proceeds in different ways in different regions that may coalesce into different sets of practices.

Spelling changes do occur in the Middle English period, but they tend to be very gradual. For instance, in Old English, the /kw/ sound was typically written as <cw>, but in Early Middle English there was a gradual shift towards <qu> spellings due to the example of words that entered the language from Norman French (often called Anglo-Norman for the variety that was spoken in England). But it took time, both for French words to actually enter into English and for English spellings to change due to that influence. But eventually, it wasn't just the case that French words like quantity, quiet, and quest were spelled with qu, but also words that were already a part of English like queen and quick, which in Old English had been spelled cwen and cwicu. The Normans invaded England in the late 11th century, but the massive influx of Norman words into the English language wouldn't occur until the late 12th and early 13th centuries, which also matches with when we see this orthographic change taking place in English. Even if we can identify the impetus for a particular change, the timespan on which the change occurs can be very large.

And this brings me to your particular questions! First up, thorn. The important thing to keep in mind is that a shift away from thorn and towards <th> was already ongoing in Middle English before William Caxton introduced the printing press to England. Here's the first page of the Canterbury Tales from the Hengwrt manuscript, which was written prior to the introduction of the printing press, and there is not a thorn to be seen on the page. The introduction of the printing press didn't cause thorn to be eliminated; instead, it accelerated a change that was already ongoing in the writing habits of London scribes and disseminated it more broadly.

In some ways, Caxton is a victim or beneficiary of a series of simplifications such that the record of what he actually did has been incredibly distorted, and a whole host of gradual changes that began before he was born and carried on long after his death have been ascribed to him. Caxton played an important role in developing a more standard form of English, but he was responding to shifts that were already ongoing in London English and in particular to writing practices associated with the Chancery. And he developed close relationships with type makers on the Continent, in particular a printer named Johann (or Jan) Veldener with whom he worked closely in Flanders and who probably made several of the type faces that Caxton would use in England. While the first typefaces used in England would have been made by people like Veldener on the Continent, there's nothing that would have prevented Caxton from commissioning letters that weren't commonly used on the Continent, and in fact he actually did make limited use of thorn. One of the forms that thorn lasted the longest in was an abbreviation for the word "the" that consisted of thorn with a superscript e on top of it, and you can actually see an example of it in the second line of Caxton's first edition of the Canterbury Tales. In this case, the abbreviation for the and the abbreviation for percid as pcid (where the p has a bar on the descender) appear to have been used to save space after "and" was unnecessarily added at the beginning of the line, though whether it was in the exemplar they were following of their own error, I don't know. Elsewhere on the page the text uses "th" instead of the thorn, so this is an exception to the rule, but the point still stands that if Caxton had wanted to use thorn more extensively, there wouldn't have been anything stopping him. And, notably, the thorn that appears here is also not the same as the letter y, which appears prominently on the third line in "euery veyne".

Nor was Caxton restricted in his career to a single type. He would print a second edition of the Canterbury Tales with another typeface that is quite clearly different from the previous one, and what's more, we can see a number of small spelling differences between the two editions that illustrate the variability of the spelling in this period.

Thorn would continue to be used in ever more restricted contexts and it would come more and more to resemble y and even be printed as a y, but this is still a matter of print reflecting, following, and perhaps accelerating scribal practice rather than bringing about a change all on its own.

At this point, it's worth mentioning that there is a big difference between the (gradual) standardization of spelling and spelling reform. Printers played a role in the standardization of spelling, but it wasn't in innovating new orthography so much as selecting a dialect and a set of loose spelling conventions for that dialect that corresponded to their intended audience. For Caxton, the intended audience was middle and upper class, what he described in his preface to a translation of the Aeneid as "a clerk and a noble gentleman." He wanted to appeal to an audience that was both large in number but also an audience that craved a sense of sophistication.

The economic argument you extend shows how standardization and reform are different. Given that thorn was already well on its way out in the dialect area that dominated the early print scene, it wouldn't have made much financial sense to produce a letterform for thorn that would have been rarely used anyway and that had ready alternatives in the <th> digraph and also the occasional substitution of <y>. Although, to be honest, I'm a bit skeptical of the economic angle here. If a printer wanted to create a typeface to use thorn more extensively, there is nothing that would have stopped them, and in fact the printer John Day in the sixteenth century would create just such a typeface that was meant to evoke Old English manuscripts that Matthew Parker used to print his edition of Asser's Life of King Alfred. You can see this Alphabetum Saxonicum if you click through to the 14th image, listed as p. x., here. However, the kind of changes that you suggest would be a much more radical intervention on Caxton's part, not using already existing spelling conventions but innovating entirely new ones. Spelling reform has a long and spectacular history of failure in the English language, from a medieval monk named Orm who invented a completely unique and fascinating spelling system that nobody else ever used to George Bernard Shaw, who left money in his will to create a new spelling system which was never achieved. While undertaking a thorough reform of English spelling to employ fewer letters and be more phonetically consistent might have lowered the cost of type and book production by some amount, it likely would have alienated potential readers, would have required a large amount of additional effort and training for apprentices to follow spelling conventions that they wouldn't have had prior exposure to, and any potential savings would have been negligible when spread across the thousands of copies printed using a particular set of type.