I don't have any experience with 2,4-DB, but a google search shows that it is used/labeled for crops (soybeans, peanuts, alfalfa). No mention of pasture. Appears that it is only effective on some broadleaf weeds at an early stage of growth. Some species controlled if they are less than 1" tall, some if they are less than 2" tall, some if they are less than 3" tall. Morning glory and cocklebur controlled up to 36" tall. So, seems like being able to use it on clover comes with some disadvantages.
Corteva has promised a new herbicide for several years that will control more weeds than 2,4-D, but will not kill white clover. Name is ProClova. So far, it has not received EPA approval. But has recently been approved in Germany. Maybe there is hope that it will soon be available in the US.
ProClova™ Herbicide Offers Weed Control While Preserving White Clover, Pending Registration
www.corteva.us