I only agree with #3. Examples #1 and #2 can be run even with RAW, and there are probably cases on the board where groups actually play that way regularly.
#3 is interesting because how you feel about 'handles it well', depends really on the degree of simulation you are interested in. D&D actually does just as bad of a job of simulating melee combat as it does of simulating firearms. What really matters is how much you care. If you are a historical reenactor of Western martial arts, you may well find D&D a terrible system for what interests you. By that standard D&D doesn't handle combat with swords well either. On the other hand, if you don't care that the PC can be hit be 15 bullets and still function as if they were uninjured, than D&D can handle combat centered on firearms just fine. D&D can be made to handle firearms as well as it handles melee combat, but this perforce requires house rules because the core rules don't in fact cover firearms. But its worth noting that DMs as cannonical as Monte Cook allowed firearms in his campaign.
I'm posting when I should be working, so forgive me in advance if this doesn't make as much sense as it should.
w/r/t Point 1. I won't dispute that you can use D&D to play a ghost, vampire, Kaiju, or disembodied intelligence. I don't think the game handles these options very well, because (a) there isn't a lot in the way of rules for doing so, and (b) non-human characters tend to upset/conflict with other assumptions in the rules about how the game is to be played.
Consider the vampire -- an iconic monster that people like to play. But the D&D vampire makes a really weird PC because of its mix of powerful abilities and crippling weaknesses. On the one hand, at-will level draining gives the vampire a huge offensive advantage. Damage reduction gives it a significant defensive advantage. At-will gaseous form gives it a powerful tool for avoiding traps, sneaking past enemies, and general exploration. Put this vampire in a typical dungeon crawl, and it is nigh unstoppable.
At the same time, the vamp has critical weaknesses. Sunlight and running water destroy it. It cannot enter private buildings. It's tied to a coffin full of dirt. These weaknesses, deform the game experience. The vamp can't meet NPC's in the broad light of day. When it travels, it has to keep up with its coffin. When it dies, it can't be raised.
And the vampire is probably the closest to the human end of the spectrum from the examples I provided. Ghosts walk through dungeon walls. What monsters from the monster manual challenge Godzilla? What does a disembodied, super-intelligent alien intelligence even do (other than torment Captain Kirk)?
w/r/t Point 2. You can certainly play a game with little to no combat and little to no risk of combat. I know a number of folks around here do. But I'd point out that there aren't a lot of rules support for, call it non-adventuring play. And what rules are out there are often fairly thin and poorly developed. Or long out of print. The focus of the rules is on adventuring. A group that isn't adventuring is ignoring big chunks of the rules (character classes built for adventuring, combat and adventuring equipment in the PHB, the combat rules, combat-oriented magic, etc. etc.) They may find themselves having to create significant houserules to do what they want (frex, creating an economic system that makes sense).
w/r/t point 3. I like guns in my D&D. I've used 'em since I started playing. But guns cause at least three significant problems:
1. D&D is built for melee combat. Many monsters lack ranged attacks, which makes them particularly vulnerable to ranged weapons. Combat in a dungeon environment takes place at extremely short range, making it hard to get off more than a shot or so before melee begins.
2. For genre reasons, which are largely illogical, folks tend to overestimate the lethality of firearms while underestimating the lethality of, say, an axe to the face. In other words, folks I know do care that an enemy can survive 15 shots from a handgun even though they don't care that the same enemy can survive 15 blows from a longsword.
3. D&D generally assumes that combatants will protect themselves with heavy armor. This causes a problem with modern settings where heavy armor doesn't really exist.