I believe Injo had no choice but to kill Kang-bin from his perspective.

‌Kang-bin basically had a strong personality. - I am not evaluating whether this is good or bad.
Before the successor was decided as Hyojong, there were discussions regarding whether the succession would follow Crown Prince Sohyeon's lineage or not.
In this situation, once the royal succession was established through Crown Prince Sohyeon's line,
if Kang-bin were to exercise regency, Grand Prince Bongrim (the future Hyojong) would have been a dead man.
Since the second son, who possessed the qualities of a great ruler, was chosen for the succession over the young grandson,
it was obvious that Kang-bin, the number one priority for legitimacy, would not remain idle. Therefore, I believe she had to be killed for whatever reason.
And Injo was the only one who could do it;
killing Kang-bin after Hyojong's accession would have carried too much political burden.