Again, it can't be overstated that Shin Godzilla is more of an apocalyptic event vs an actual living creature with a precise goal.
This scene was cut, but you can easily see how it'd be canon considering the tail shit.
The chunks of flesh being blown off of him were beginning to become their own life forms with teeth and eyes for fucks sake.
Who knows what that tail is going to become the next time he wakes up?
Doing damage to Shin Godzilla was just giving it another avenue of evolution ultimately.
What do you do against a creature that spawns more horrifying madness from the wounds you create on it that it ultimately heals anyway? lol