I think a situation where you genuinely have to fight a patient is so rare as to be almost nonexistent, and the situation existing means many things failed to reach that point.
A good inpatient unit or ER has a lot in place to avoid getting to that point, such as:
-Designs that allow for good visibility (for example nursing station staff can see most of the unit)
-Searching all patients for weapons coming at their point of entry to the hospital
-Team observation and communication when a patient shows warning behaviors (anger, grievance, posturing, etc.)
-You observing carefully for signs of escalation, and being mindful when a patient might want to assault you (for example a particularly nasty hold)
-Generally ensuring other staff are around, especially when seeing a potentially violent patient
-Avoiding having a patient between you and an exit (patient in the doorway with you in the room, patient cornering you in a low-visibility part of the unit, etc.)
-De-escalating when signs of agitation arise, using the many skills of verbal redirection we develop over time and avoiding "kicking the hornet's nest" / being tone deaf to the developing situation
When things do get to the point of assault if we are talking an elderly patient taking a swing at you, or a young psychotic man shoving you, the strategy if at all possible is to remove yourself from the situation ASAP. Attract attention and move. Fist fighting the patient should not be on the menu at that point.
But with all that said, I have heard of situations where the swiss cheese all lined up and a provider found themself in a serious struggle. For example, I knew one ER psychiatrist who had no suspicion a patient would become violent. While walking out of the room the patient quickly jumped up, got him to the ground, and started full-force choking him. Other staff made it there pretty quickly to assist and no permanent physical harm was done (but plenty of psychological harm!), but this is obviously a dangerous situation.
In those extraordinarily rare situations (that for most of us should not happen in a career, but unfortunately do happen at times) using any amount of force necessary to preserve your own safety is the right call. If a strong young man is on top of you choking you with no help present, gouge his eye, try to knee his groin as forcefully as you can, bite, or do anything else you have to to preserve your own life. I think because most of us are (thankfully) removed from life-threatening violence in our daily lives and because situations posing imminent risk of killing or permanently disabling us are exceedingly rare, we forget that in some extremely unusual situations serious violence can be the right response. The book "When Violence in the Answer" provides an interesting overview.
But I think the tl;dr is most of will never and should never physically fight a patient, but for the very rare provider who finds themself in a genuinely life or death situation I hope they recognize it for what it is and respond in any way that keeps them alive. I think every healthcare provider has the right to genuine self defense and the responsibility to avoid reaching that point with every tool at their disposal.