Sunflower

Pick wild ones for what falls out of them, not for the flower. The seeds are the part with a future. The bloom that lands in your inventory has no recipe, tea or pie on the site waiting for it, and the game's whole description of it says it is very tall.

The catch shows up on a seed run. Say you sweep a meadow on the way home, picking every sunflower for a shot at sunflower seeds. Seeds stack to fifty, the flowers only to twenty, so the blooms spread over slot after slot while the seeds sit in one. By the time a barrel turns up by the road, half your bag is flowers.

Drop them, or carry them home to the composter if you farm anyway: spare crops go in there with the rest of the scraps. If you like the look of sunflowers, grow the plant itself and keep a clone of a good one. The bloom in a planter is the pretty part, and it stays pretty only until someone picks it.