Hey I just remembered one. Slipped my mind because it’s not exactly mouse and keyboard (but you could 100% do it with mouse and keyboard.)
The Wii game Sin and Punishment: Star Successor is a run and gun that uses the nunchuck for your movement, and the Wii remote as your pointing device for where your character aims. The perspective shifts over the course of the game, sometimes it’s a rail shooter, but for a large chunk of the game it is a 2D run and gun.
I highly recommend it. It’s by Treasure, the studio you might know as the creators of Gunstar Heroes and Ikaruga.