There's a difference between "can do successfully" and "the mechanics really evoke and support the setting."
There's also an axis from "unmodified D&D" to "a different system that supports the feel I want", and modding D&D is moving along that axis toward the second one already.
Can I run anything I want in unmodded D&D? Eh, sure. But that doesn't mean that there are places where the mechanics either lets you down or actively fights you in evoking the flavor of what you want. At that point mods can hit some low hanging fruit, and table buy-in to gloss over other issues can go a long way.
But that doesn't mean that a system designed from the floor up won't do a better job.
I'll take a fairly extreme example just to show off differences: Consider Don't Rest Your Head, a game about being awake in your dreams where you get both more powerful and more vulnerable as your get exhausted. It's a lot about exploring your psyche and your choices. With mechanical support for that exploration.
No one is putting down 5e - it's a great system. Every system has things it natively supports better.