I've been mulling this question over a for a while and, though I'm still formulating a full answer, I'll put my thoughts down here.

First off, here's the full quote from Jomini:

I cannot affirm positively which of these methods is the best; for I have not seen them used in actual service. In fact, in real combats of infantry I have never seen any thing but battalions deployed commencing to fire by company, and finally by file, or else columns marching firmly against the enemy, who either retired without awaiting the columns, or repulsed them before an actual collision took place, or themselves moved out to meet the advance. I have seen mêlées of infantry in defiles and in villages, where the heads of columns came in actual bodily collision and thrust each other with the bayonet; but I never saw such a thing on a regular field of battle.

While I haven't read the book the article cited for the 2% figure, it doesn't surprise me. Wounds from bayonets in the American Civil War, for example, were 0.37%, while the overall rate of wounds from bayonets in European wars between 1854 and 1874 was 2.4% (though with an extreme of 22.3% for the Second French intervention in Mexico). However, I have seen it argued (mostly on internet forums) that the figures for the wounded downplays the actual combat effectiveness of bayonets, as they don't include figures for those killed on the battlefield, just those who were treated by the doctors. Bayonets, targeting vital organs, were more likely to kill than bullets or shrapnel from shells.

On the other hand, according to Dave Grossman, the melees of the Civil War were fought with rifles used as clubs far more often than with their bayonets, while Jomini (as noted) and Ardant du Picq notes that battle with bayonets is "extraordinarily rare". The only example he knows of where sustained bayonet fighting occurred between two lines of infantry was at Amstetten, but that "Even then the Russians gave way before the moral and not before the physical impulse. They were already disconcerted, wavering, worried, hesitant, vacillating, when the blow fell. They waited long enough to receive bayonet thrusts, even blows with the rifle (in the back, as at Inkermann)." Baron de Marmont, my favourite Napoleonic era general, records a few other cases where bayonet fighting occurred, but they all refer to the situations where Jomini has observed bayonet fighting.

This brings us around to your question: if infantry in gunpowder era armies wouldn't stand and receive a bayonet charge, why did pre-gunpowder era infantry stand and fight in hand to hand combat?

There are a few important factors, but the most important of them is armour. As J.F. Verbruggen has pointed out, the Rule of the Knights Templar allows foot sergeants without any armour to withdraw at will, without any shame on them, but foot sergeants with armour and knights were forbidden from retreating so long as there was another Christian banner on the field, on pain of expulsion from the order. Similarly, in the 12th century chanson de geste, Le siège de Barbastre, wearing armour is seen as something which should boost the bravery of a man "I know full well that you are a coward:/Your coat of mail is neither pierced nor torn,/And neither your head no arms are wounded."

Whereas a 19th century infantryman had nothing that could prevent a bayonet from penetrating his vital organs, even the poorer men in a battle in the Early and High Middle Ages would have a shield, which is a barrier between themselves and the weapons of their enemy. So long as it's between them and the enemy, they have at least some hope of surviving the initial encounter and so are more likely to stand and fight. Additional armour increases their chance of survival and so "diminishes the dominating moral effect of fear", to quote Ardant du Picq.

Another important factor is unit cohesion. This has two parts, the relationship factor and the mob factor. In the relationship factor, most levied foot soldiers or dismounted knights would be fighting with friends or family around them. Or, if not friends or family, then people from the same community. It's a fairly well documented phenomenon that soldiers from the same unit who hate each other will almost always take the side of the other in an argument with soldiers from a different unit and can put aside differences in battle. Having some sort of relationship with those around them will help bond a group of soldiers together and make them less likely to break and run.

Even when men fighting together have no familial or locational relationship, those who fight together will develop the comradeship when they fight together for a time, much as modern soldiers do. I have heard some people argue that the modern notion of comradeship cannot be applied to the past but I believe this quote from Jean V de Bueil's Le Jouvencel does indicate this kind of bonding between medieval fighting men:

It is a joyous thing, war...You love your comrade so much in war. When you see that your quarrel is just, and your blood is fighting well, tears rise to your eyes. A great sweet feeling of loyalty and of pity fills your heart on seeing your friend so valiantly exposing his body to execute and accomplish the command of our Creator. And then you are prepared to go and die or live with him, and for love not to abandon him. And out of that, there arises such a delectation, that he who has not experienced it is not fit to say what delight is. Do you think that a man who does that fears death? Not at all, for he feels so strengthened, so elated, that he does not know where he is. Truly he is afraid of nothing.

The second part of cohesion is the mob factor. This plays in with the social factor and shields, because there is a huge psychological benefit to the "shield wall" formation. As the name implies, a shield wall is practically a defensive structure. The Anglo-Saxons had a number of terms for this "board fence", "board wall", "shield fortification", "shield wall", all implying that the shields were a vital part of an army's defence. In a very similar manner, Wace describes the Anglo-Saxon shieldwall at Hastings in terms of being a literal defensive wall.

In battle, men would habitually draw close together out of fear by default. For example, at Darum in 1180, "Terrified because they [the enemy] were so powerful, our men began to draw closer together, as they had been trained to do, indeed so closely that they could scarcely carry out an attack because of the mass." Even some of Caesar's experienced legions at Sambre, hard pressed by the Nervii, were "so closely packed that they hampered each other for fighting". This was after almost all their centurions and officers had been killed and there was no one there to keep order and prevent the legionnaires from grouping up too much.

This drawing together adds psychological mass to the formation, making it harder for men to retreat and, in the advance, pushing those in front forward as those in the rear, not being as close to the battle and so not in immediate danger, push forward. The push isn't inexorable - it can be stopped and almost certainly slowed to a stop before it reached the enemy line, but it did push forward initially and prevent retreat from the front ranks. Combined with social ties and the psychological effect of shields and/or armour on reducing fear, it reduces fear enough that the two sides will almost always come together for a fight.

Beyond this, we come to the motivation to stand and fight. Shame is a big factor in this. Other than the shame of abandoning friends or family, there's also the shame to be felt at being a coward. Even in the early 19th century, when English society was more a Guilt society than an Honour society, not being seen as a coward was very important to the English officers, who would return to the fighting even when badly wounded or would try and hide their wounds so that they could fight. Back in the Middle Ages, when honour was even more important to men, this would have been an additional factor in preventing men from breaking and running from the enemy. Though, of course, shame alone would not have prevented the men from running had the other factors noted above not been in play.

Another factor in motivating men to stand and fight is that of good leaders who are able to encourage their men to hold that little bit longer, to attack a little bit harder, who can lead by example, to start an attack when all seems hopeless and shame their men into attacking with them. As seem with Caesar and the Nervii, the leaders prevent their men from becoming a confused mob, they keep them ordered and give them the encouragement needed to stay in ranks spread far apart enough that they can fight, but also close enough together that the enemy can't penetrate them. Without some sort of leader providing encouragement to the men, they will inevitably crumble.

(1/2)

This is a very good question and there is always more to be said about it, but you might be interested in this previous post.

The musket a bayonet is attached to can be pretty scary itself if not more so. The closer it gets the more damage the bullet is going to do and the less likely it is to miss, no matter how inaccurate the shooter. As Ardant du Picq put it in 1870, when near the enemy "Imagination always sees loaded arms and this fancy is catching."