As you've already seen there are many different opinions on using a red dot on a shotgun. It depends on the intended usage of the shotgun. If it's going to be used entirely at close range such as in a home defense setting, it maybe alright to go with no red dot. I have a Remington Tac 13 that would probably fit into that category perfectly but I just set up mine with a Holosun 510C-GR and I love it. It makes fast acquisition of the target easy with the circle and dot reticle. Granted, for close range with something like the Tac-13 you could probably do without, but it's also very workable with although I might eventually try something smaller.
With my Benelli M4 I have it set up with a RMR. It works great either way, for relatively close up shots with buckshot, or for longer shots with slugs. For longer shots it's a lot faster than using the stock ghost ring sights, for me anyway. I think most people will also see that as their eyes age, it's also so much easier and faster to use a red dot instead of relying on the standard sights. I think you'll find that all of the advantages of using a red dot on a rifle apply to using a red dot on a shotgun. Unlike Hollywood movies, shotguns do not just spray a pattern of shot all over the place. Careful placement of your shot is important.
So I say do it, you'll be happy with the setup.

So I mounted the Crossfire and took it out to the hayfield this weekend. I like it. My SuperNova is the version with rifle type sights, the red dot makes target acquisition much faster. I put about 35 rounds of mixed buckshot and slugs downrange, the Crossfire seemed to handle the recoil fine. I was a little hesitant about putting an inexpensive Chinese product on the shotgun but it seems to work for now. I likely will replace it with an Aimpoint Micro when prices come down and I get a bit of extra cash but this will work in the meantime. Bottom line--good to go.