I do indeed wonder why do they care about ICC considering they did not recognized it. One reason is that in fact that some of this "great powers" are much more "weaker" than they pretend, and that someone exposing something bad that they do will still have some effect on them.
Or (not sure if better or worse), they the "great powers" are stupid and they did not hear of the "Streisand effect".
Because they know full well that even the existence of the ICC is a threat to them, it allows people to point out that they have not subscribed to the fact that this court exists and that should have a power that they've been denied. If the court did not exist at all they could pretend to be like every other country.
Because 165 countries are signed on to the Rome Statute and are required to arrest war criminals (as deemed by ICC) like Netanyahu if they step foot in their country.
Or (not sure if better or worse), they the "great powers" are stupid and they did not hear of the "Streisand effect".