I've been watching HEMA videos, and it's quite interesting how little resemblance fighting with sword/spear/shield on TV and in movies has to the real thing. I am not a HEMA practitioner, however here is a some of what I've gleaned from their videos:
No one sane would take off their helmet in the middle of a battlefield for the most important fight/battle. You don't slice with a sword through plate armor or decent chain mail. It just doesn't happen in real battle conditions. For that matter, it's not so easy to slice through padded cloth gambeson armor! Also, the "reality-tv" shows that have covered historical weapons are often bogus. You "half-sword" to wrestle your opponent to the ground, then guide the stabby point of a specialized sword through an eye-hole or other gap in their armor. Likewise, real battles between knights didn't consist of them bashing at each other, using their swords crudely like glorified metal clubs.
Long exchanges of blows/parries in movies are just for show. In fact, there are fighting manuals that urge you not to parry if you can help it, but rather always "bind" a weapon in the process of some kind of counterattack.
Social class meant a hell of a lot. On the battlefield, it determined how much armor you could afford to keep up, which made a big difference to how likely you'd be killed.
Most swords were sidearms, not main battlefield weapons, analogous in role to an automatic pistol vs. an assault rifle. For most of western history, and in many other parts of the world, the main battlefield weapons were polearms, often used in conjunction with a shield. This even applies to a certain extent to Japan! (Though the naginata fell out of favor and for awhile actually became a sign of social status for women.)
Katana are not magic, and there were and are european, middle-eastern, and indian subcontinental swords capable of equivalent feats of cutting.
In the movie "The Lion in Winter" there is a fight scene that is quite similar to what you describe as accurate. It's actually quite disturbing, as it depicts the frightening amount of intimacy involved in wrestling someone to the ground, pinning them to the ground, and then struggling to stab them to death. Not exactly the glorious victorious violence depicted in most movies.
If you want disturbing, try the "Hardcore History" podcast where he explores the personal implications of what we know about being on the losing side of the Battle of Canae. Very disturbing, and even backed up by archaeological data.
However, in contrast to the D&D inspired popular view, warhammers and maces were specialized anti-armor weapons, not an alternative general sidearm. If you were going to carry a end-weighted weapon, it might as well be an axe. You get the same sort of momentum advantage, plus the benefit of an edge. The popular view of battle axes is also waaaay out of line with reality.
I assume these wounds described of a 1689 battle were from Scottish claymores:
"Many of General Mackay's officers and soldiers were cut down through the skull and neck to the very breasts; others had skulls cut off above their ears like night caps; some soldiers had both their bodies and cross-belts cut through at one blow; pikes and small swords were cut like willows..."
But were those through steel helmets? I really doubt that! I'd first believe there's a little hyperbole here. Also, cutting pikes is quite a different matter than cutting many other kinds of spear. Pikes were extraordinarily long, thus harder to move out of the way. Spear shafts can be cut, if they are anchored, but are much harder to cut if held in the hands. Pikes were sometimes used butted against the ground and the foot of the pikeman.
Skallagrim did a recent video which shows that a held (not anchored) spear shaft is pretty hard to cut in one blow. However, it's quite possible to destroy a spear if 3 or more cuts are placed in close proximity, even when the spear is held in the hands. I would guess that's what the author is talking about.
No one sane would take off their helmet in the middle of a battlefield for the most important fight/battle. You don't slice with a sword through plate armor or decent chain mail. It just doesn't happen in real battle conditions. For that matter, it's not so easy to slice through padded cloth gambeson armor! Also, the "reality-tv" shows that have covered historical weapons are often bogus. You "half-sword" to wrestle your opponent to the ground, then guide the stabby point of a specialized sword through an eye-hole or other gap in their armor. Likewise, real battles between knights didn't consist of them bashing at each other, using their swords crudely like glorified metal clubs.
Long exchanges of blows/parries in movies are just for show. In fact, there are fighting manuals that urge you not to parry if you can help it, but rather always "bind" a weapon in the process of some kind of counterattack.
Social class meant a hell of a lot. On the battlefield, it determined how much armor you could afford to keep up, which made a big difference to how likely you'd be killed.
Most swords were sidearms, not main battlefield weapons, analogous in role to an automatic pistol vs. an assault rifle. For most of western history, and in many other parts of the world, the main battlefield weapons were polearms, often used in conjunction with a shield. This even applies to a certain extent to Japan! (Though the naginata fell out of favor and for awhile actually became a sign of social status for women.)
Katana are not magic, and there were and are european, middle-eastern, and indian subcontinental swords capable of equivalent feats of cutting.