There was a huge lack of bayonet use during the US civil war, which would have been exploited by heavy cavalry in Europe. Bayonets were seen to be ineffective as a weapon during and after the Civil War due to the lack of soldiers wounded by them. As well as bayonets being used as tools rather than weapons, like the smallswords uses by Europeon infantry in the Napoleonic Wars, they sometimes weren't brought into combat. This could have led to a perceived vulnerability by the CSA towards cavalry, because the pike is an effective anti-heavy cavalry weapon, but hugely vulnerable to the firepower used by infantry and cavalry alike.

I can't find many mentions of cavalry closing to melee in the Civil War, partly because many Confederate cavalrymen carried extra revolvers over a sword and the Union had repeating rifles and breach-loading carbines, allowing them to hold out against skirmishers. This led to cavalry acting more like dragoons from earlier times, using the horse for mobility and dismounting for fighting.

So the pike would not have been an effective weapon on a US Civil War battlefield, but a means to short term arm volunteers until firearms could be procured. I can't academically source this, but I recall reading someone theorising that pikes would be given to a new volunteer so that they would be armed and not leave, so that they could be equipped with a looted gun off a battlefield later.

While this isn't my specialty, the subject does come up occasionally in the Civil War histories I've read. I'll try to give a general answer, but I hope you get one of our weapons folks in for a better one!

"I thought pikes were made obsolete with the advent of the firearm, especially with artillery?" Sort of. It would probably be more accurate to say that early firearms still left soldiers vulnerable to the kind of attacks that pikes were designed to counter or deter. Early muskets had to be reloaded after each shot, reloading wasn't a quick process, and the soldier was vulnerable during it. Armies devised strategies to get around this -- most notably, having one line of soldiers firing, one line behind them reloading, and another line preparing to fire as the first line retreated -- but cavalry charges were still dangerous.

Pikemen were employed to protect musketeers against enemy horsemen, but they were less and less useful as muskets grew more powerful. However, the addition of bayonets in the mid- to late 17th century was really what made pikes obsolete. When a musketeer could convert his weapon into a spear very quickly, there was little point to soldiers on a battlefield being armed only with a dedicated short-range weapon.

Artillery could do severe damage to massed infantry either way, but even by the American Civil War it was nowhere near as mobile or accurate as it is today. A number of Civil War battles were also in heavily wooded, rocky, or hilly areas, which minimized both armies' ability to deploy artillery easily or effectively.

Confederates and pikemen: This is actually true. Stonewall Jackson did indeed order pikes for his men while he was outfitting his corps, although he wasn't the only person to suggest it. (The governor of Georgia also ordered pikes for the use of the state militia.) In one of his later letters, he justified it by saying that the Confederate supply chain wasn't great at reliably providing ammunition or replacement rifles (also true), and pikes would provide a means of advancing on a position even if the men ran out of bullets. Jackson was famously aggressive on the field and actually ordered a court-martial for one of his brigadier generals, Dick Garnett, when the latter ordered the retreat of the Stonewall Brigade when they were surrounded on three sides by Union forces and out of ammunition.

In fairness to the outwardly-crazy people: It has to be said that the idea of using pikes (or at least keeping some in reserve) isn't as bizarre as it seems, largely because Jackson: a). was familiar with the terrain on which the Army of Northern Virginia did most of its fighting, and: b). knew that bayonet charges could be very successful in the right context. While the experienced officers on both sides of the conflict had largely been trained in Napoleonic tactics, most Civil War battles didn't take place in open fields. You know that artillery comment above? The same applied to the infantry. The majority of Civil War battles weren't two armies facing each other across an open field, as was typical of Napoleonic warfare; the ubiquity of hills, streams, and woods in the eastern U.S. made relatively close-quarters fighting fairly common just to be able to see the enemy at all. The rationale behind a bayonet charge under the circumstances was to advance while firing, make use of any cover afforded by the terrain, and then rush the enemy with bayonets, denying him the opportunity to fire or quickly reload.

That was, for better or worse, exactly the kind of tactic you'd expect to see from Jackson, and for someone who maneuvered as quickly as he did against inexperienced and/or often incompetent Northern generals, it could be very successful. It's not hard to see the logical leap from the use of a bayonet to a pike. However, if you were an ordinary soldier on the ground, you'd quickly see the problems with it. Trying to maneuver a long pike through thick woods would be a huge nuisance, they'd be very unwelcome weight on the lengthy marches for which Jackson was equally famous, and there was no safe or sensible way to advance on an enemy with a good defensive position if they intended to stay and fight. Ordering infantry assaults on fortified positions was one of the most consistent and tragic leadership mistakes of the war on both sides, and there have been quite a few historians who've wondered how Jackson would have fared in posterity if he'd faced the more grim and experienced Northern military leadership later in the war.

As an additional note, Civil War soldiers on both sides of the conflict were largely volunteers or (later) conscripts without much quality training, and soldiers in those circumstances have historically been very reluctant to use blades to attack. Even in battles with bayonet charges, injuries from the blades were fairly uncommon, and something around the order of 2% of the casualties observed in the field hospitals.

To the best of my knowledge, pikes were never actually used in any Civil War battle, so Jackson's death had little to do with it. Unfortunately, I do not know if Lee himself ever directly commented or gave an opinion on the pike issue.

You'll have to give me a little time to dig up the books I used for this (not my specialty, so I have a highly imperfect command on which bits of info come from which book, sorry!), but I do remember commentary on the pike issue in Stonewall in the Valley, which is about Jackson's Shenandoah campaign.