My last first aid course didn't mention tampons specifically, but if you need to stop heavy bleeding, anything is on the table.

We were told that the general practice with a major wound was essentially to use a rolled up bandage to wipe the worst of the blood away so you can see where it's coming from, then put said bandage over the probable artery and apply lots of pressure.

Your job as first aid is to keep someone alive until paramedics arrive. Tissue damage from a tampon gluing itself in can be fixed. Total blood loss less so.

They did say they're an option for a major nosebleed though.