A French company (SilMach) backed by Timex Group is claiming to have opened a new chapter in watchmaking with the creation of a silicon motor that matches the accuracy of quartz-based movements with the elegance of a mechanical watch’s sweeping hands.
Higher beat quartz watches do exist, like Bulova’s Precisionist watches (which I believe do beat 16 times per second like you mention).
My understanding is that they are not more common because moving the hands more frequently like this uses battery a lot faster, so the watches either need to be bigger for more battery or require more frequent battery changes.