So the letter form þ was not exactly abandoned suddenly.

First, the þ was not consistantly used even throughout late medieval English written texts. Spelling wasn't standardised and depending on the scribe you'd get for today's <th> the spelling <þ> or <th>, or both forms alternating without rhyme or reason.

So, the first printing types were imported for printers in England (William Caxton, Wynkyn de Worde and Richard Pynson), mostly from the continent with countries such as Germany as indicated by Hill in 2016 (England only gets its own first type foundries in the first quarter of the 1600s). You mention Gutenberg, but bear in mind that being German, he wouldn't have needed the thorn letter: even his famous Bible was printed in Latin (which also does not use the þ). There was no incentive for type foundries in Germany for example to create these at first.

So, it is very unlikely that the early printers I have mentioned above had access to the þ typeface at all. A rare example of a font cut in England featuring letters from the Anglo-Saxon Alphabet was the one created by John Day for the Archbishop Matthew Parker in 1566 - that's very late!

Plus, as I mention in my first paragraph, it wouldn't have been much of a problem due to the non-standardised spelling anyway in the late 15th and Early 16th century, and using <th> wouldn't have been an odd choice at all. The spelling was already common and those letter types (<t> and <h>) were readily available. For brevity, some printers would have to abbreviate the article <the> in first position in the sentence with the majuscule letter Y (the shape of which is reminiscent of the thorn, especially in its capital written form), and a superscript <e>, thus forming <Ye> which is read as <the>. You probably already know this but that's how nowadays you find some pubs called "Ye Old Place" due to this influence (where <Ye> is supposed to be read as <the>).

If you want to read a bit more about the standardisation of written English during that period, I recommend the chapter written by Vivian Salmon in The Cambridge History of the English Language Volume 3. 1476–1776 (partially viewable for free on Google books).

I also highly recommend English in Print from Caxton to Shakespeare to Milton by Valerie Hotchkiss and Fred C. Robinson (2008) if you are curious about the relationship between Early English printing and language!

On English typography, there is also Hill, W., Typography and the printed English text in The Routledge Handbook of the English Writing System (2016).

If you're curious about the type foundries in England, this article is useful: Barker, Nicolas. “The Old English Letter Foundries.” The Cambridge History of the Book in Britain, edited by John Barnard and D. F. McKenzie, by Maureen Bell, vol. 4, Cambridge University Press, Cambridge, 2002, pp. 602–619. The Cambridge History of the Book in Britain.

Edit: some phrasing mistakes at the beginning. Edit2: Thanks for the awards, people!

This question cannot be read aloud by screen reader software. Here is a plain text version:

Subject: In English writing, was it mainly the early printing press not having a thorn character sort that caused the trend of only using Th instead of the thorn character or were there other factors involved? Why abandon such a useful and common letter?

Body: In an era when saving space was seen as important, when printing costs were high, it seems like the letter thorn would've been prioritized more. Didn't Gutenberg ever think to make a thorn sort? It's not like the English weren't buying printing presses too. Would it really have been too much effort for him to include one more measly letter for us English speakers?

It's very strange how the English letter thorn exists in ancient manuscripts & a bit on the internet but it skipped the print era completely. Laugh emoji.

Note: Many comments also include characters that are not pronounced by screen reader software. If anyone is using a screen reader and wants to know more about the comments, I can provide a translation.

OP’s writing brings up another question: what happened to the long-S? It was used in handwriting longer than thorn was, as it’s in the US constitution. Why did it fall out of favour?