The issue, IMO, was the major difference between the European and Chinese writing systems and characters.
The printing style that you describe, which was developed by Bi Sheng if I recall correctly, used clay pieces with single characters on them, and this passed in China because a page of their text results in far less individual characters than with any European script.
So, in Europe, you would need many more character pieces for any single page, imagine writing an entire text block in German by using these;
https://i.imgur.com/yv4DKnC.png
Now, I am not saying that this could not have been revamped and gained advantage of in Europe, but I do consider that having a dozen men in any monastery available to just write and copy stuff by hand for several hours a day minimized the need for printing anything in the quantities that they were used to requiring.
Or perhaps the issue was straight up rejection, it was the case that printing presses were not received well by a lot of religious figures.
Even destroyed en masse by them in some parts of Russia and even the Ottoman Empire.
Hell, the first printing press in Arabic was not constructed until the 18th century because before that printing in Arabic was seen as blasphemy and punishable by death.