non-indie beat em ups are rare, the problem is that the genre evolved to today's hack and slash and stylish action games, and musou. It doesn't have to be a belt scroller, but there is still a joy in just beating the crap out of random thugs. Like you said Yakuza really hits that spot well. That and Dragon Crown which was influenced by the Dungeons and Dragons game.
Like-wise run and gun is hard to come by, and I mean that as pure fast-paced shooting action. That also moved on to third person shooters (which usually have cover) but you can see a little of gameplay in action platformers like Ratchet and Clank.
I would love to have another game like Gungrave personally, it was wild and a lot more fun than most shooters I tried. Sin and Punishment for the rail variant.