When value boxes get small, we change from a "left center" layout to a "top right" layout. Turns out that, the right portion of that just happens to work when you put icons (which have margin-left: auto) in the showcase, but if you put something else, like text, the showcase is centered:

library(bslib)

page_fixed(
  value_box(
    "Title", "value", showcase = span("showcase"),
    style = "width: 275px; resize: both"
  )
)