You said, "[M]artyrdom did nothing for the Church in Japan when it was closed to foreigners. The Church disappeared."
How did we get from there to "tak[ing] the place over"?  The Church in Japan survived and grew, with traditions, including the Rite of Baptism, continuing.  There existed a thriving underground community of believers.  In yet another variation, the same example is being made in China.
Perhaps you didn't mean that unfortunate choice of words ("did nothing" and "disappeared").  Had you simply corrected it to "went underground" or "into hiding", that would probably not engender any disagreement.  Disappear can mean both "vanish" and "cease to be".  But martyrdom did "do something" for the Church in Japan, just not in the same form as in the West.