My feeling is if I can render at 4K I can just not do AA at all. It really looks quite fine without, at least for me.

Yes, on high density displays this is very much possible. Eye based SSAA, the worse your prescription the better the quality. On my Pixel 9 Pro, the no AA circle demo is perfect on native 1440p resolution without AA. But dense foliage in 3D scenes will definitely ruin that. Motion induced shimmering is inescapable I think, without some kind of filtering.

No AA on 4K/high-DPI has been almost perfect for me, but I still occasionally notice thin edges flickering and objects getting dithered when fading in or out. It's definitely better than TAA though, which just ends up smearing everything that moves.

I tried that initially, but I found that it still wasn't quite satisfactory. My game's art style has a lot of straight edges, to be fair.