Related?
In preparing for a particular hunt on large, tough herd animals, I chose an HP for the first shot (not for follow-up shots). The two chief reasons were:
1) To keep the bullet from exiting the animal, and possibly injuring another in the herd.
2) General opinon from experienced hunters that the HP would deliver more of a "whack" to the animal, which might convince him to fold on the spot (so long as he wasn't already on high alert when I shot him).
"Increased damage" as a reason was not on my radar: I knew a non-HP solid bullet, well-placed, would damage him plenty. In fact, solids were my planned back-ups, the ones I'd depend on if things went sideways.
Results: As to #1, I can say that worked out well. As to #2, one animal crumpled in place, one ran (but not too far). Both good chest shots.
Police will not be shooting any suspects "by surprise", so I'm not sure #2 applies to them. However, a private citizen might encounter an attacker who didn't know the intended victim was armed, and may be very surprised indeed to find himself shot.
FWIW.