The most obvious examples are emoji which may need hundreds of strokes in many colors to be properly colored as we see them in most places (that aren't HN). Many emoji were rendered as bitmap images on many platforms to be able to get the colors correct prior to font support for color fonts.
Search engine parsing: image "alt" tag should be equivalent again.
Copy-Paste: Arguably not better with a font. A raster image will be the same regardless of where you copy-paste it. A logo implemented with a font will only look the same when copy-pasting between applications that are aware of that font. If every company creates their own font-logo, it will just break copy-paste everywhere except their domain.
If I embed an image in some text, like `foo <img alt="bar"> baz` then I doubt any search engine can find this for the search query `"foo bar baz"`.
I would like to copy and past text-like things as text, without having to copy and paste images. When I want to copy and paste text, I rarely care about matching exact styles. In cases where I want the exact style, I can just screenshot.