The pump shotgun is a very legit HD weapon and for the reasons you listed.
I keep one here. A no frills Mossberg 500c 20ga. I keep 3" #3 buck mags in it. My 95lbs wife has no issues with recoil out of it with this round.
In this round there are 19 .20 cal pellets. 100% devastating at 25". Shooting a 4'X4', 3/4" mdf board, It will dam near take an 18" chunk out of it.
Me, personally, I would have opted for the 12 ga but I also needed the wife to be able to use it as well. The 20ga worked out perfect.
Hopefully she(we and you to) will never need to use it.
Now for the .50BMG....
At 1k yds, a 30 cal(.308 win.) will actually do some good damage on a chunk of ballistics jel but unless you place your shot very well, the target may live through it. An upper center mass hit should/will end its day with a .30 cal.
The .50BMG, on the other hand, makes a 24"X24" ballistics jel target turn into a jig saw puzzle! IMO, even out to 2k yds, with a .50BMG, any main body hit will be life ending. All you would need to do is hit the target.