1) Its not horsepower solely; its also torque.
2) An engine like the Vic's is preferred because of wide, cheap parts availability and ease of maintenance.
3) Avalons don't seem to offer anything special in terms of anything a law enforcement agency would want. I've heard Volvos were well-liked in early rounds of testing by Miami-Dade and other agencies, but price was a big factor against it. Even so, apparently they handled and accelerated magnificently. I don't see the sloppy Avalon doing that well.
4) Crown Vics are really half-trucks compared to any other car today and while BOF is old, outdated, and heavier than necessary for most applications, for police work, its ideal. Its less refined and rougher, therefore able to pop curbs and the like more than most unibody cars probably would. You and I don't need this capability, but the police do. Vics are also f-ing massive, which makes them great ramming cars.
5) Impalas you see in police duty are great for certain purposes, for example, a smaller agency mainly involved with urban and suburban environments. If your squad is predominately sitting, idling running a speed trap or DUI checkpoint, you don't need to outright power of a Vic.
6) Impalas can be picked up super on-the-cheap and guess what? Cops don't give two shits about how switchwork feels and the textures under the dash, so where the Avalon excels is irrelevant and its price is a hindrance.