My thoughts as an OB nurse - yes, it's possible with inappropriate forceps use. Any kind of instrumental delivery has risks. They used to think that a vacuum carried less risk, but I found that under the use of a skilled clinician, forceps are actually safer and more effective. I think in the 90s, forceps went out of favor and may OBs who did their residencies in that era were not skilled in their use and didn't feel comfortable using them. At a private hospital I worked at, of the 8 OBs, only ONE was skilled and comfortable in using a forceps. When I started working at a teaching hospital a few years ago, I found that all the residents are taught how to use forceps safely, and it was always the go-to, not vacuum. The only times I saw a vacuum used was during C-sections. Forceps have a place and should not be banned.
That said, I have seen and heard of some forceps injuries, both lesser and catastrophic. I personally have seen infants with facial nerve injury due to improper placement of a forceps. A nurse friend told me of a case where the doc was using forceps on a twin, and pulled so hard he internally decapitated the infant. Clearly, a totally egregious misuse of a forceps.
I remember being in a delivery where the doc was using forceps and the baby's head shot through the perineum so quickly that it totally split her perineum open, and the "POP" noise it made, made us all think that the baby's head was pulled off. I literally thought that is what happened for a moment. Thankfully, the baby was fine, but the woman had 4th degree tears.