It seems to me that with cannons and other artillery on the field, having lots of soldiers closely grouped together makes it rather easy for a well-paced cannonball to demolish an entire regiment. Was artillery still too primitive to take advantage or am I wrong in assuming how tightly-packed the infantry would be stacked during engagements with artillery batteries?
The thing here is that infantry regiments typically marched in columns and formed rows in battle. Formations were not as tightly packed as you would believe because the primary purpose of these formations were to present the greatest amount of rifles to bear to the enemy over the maximum effective area. Thus the line would be two or three deep and this reduces the likelihood of a cannonball scything through the ranks, although it was likely that this was a fairly regular occurrence, particularly if the ball skipped upon impact.
Just think logically about this; there were not that many artillery pieces per soldier even as we enter Napoleonic periods. Looking at the Battle of Austerlitz, arguably Napoleon's greatest victory, there was only one cannon per ~230 of Napoleon's men and only one gun of Napoleon's per ~482 of the Russians. That's one of the largest battles though; look at the Battle of Blenheim in 1704 and there was like 60-70 cannons per side with armies over 50,000 men strong. Cannons which, even into Napoleonic times, were usually just projectiles (ie: cannonballs) or if they did explode did not have percussion cap fuses but had to explode at preset distances. This made it very clunky.
So really a general had two options: the traditional manner of spreading out these guns across tens upon tens of thousands of soldiers, leaving entire battalions fighting with 1, maybe 2 cannons on either side or concentrating them all in one spot. The former was what most people did and, well, when you consider say 3000 people meeting on the field 1 or 2 cannonballs coming out every minute or two hardly seems like the devastating game changer you think. When it's call concentrated that means, ultimately, everywhere where the battery is not firing is, well, not being fired upon and is free to do what they wish.
Ultimately artillery was extremely useful and it's why the numbers of them kept shooting up. It's what allowed Napoleon's tactics of force the enemies reserves to commit, strike hard at their weakest link with the grand battery and then throw your own reserves in column at the faltering point worked so damn well. It was devastating, artillery was devastating. However it didn't necessarily negate the power of grouped up bayonets charging a faltering enemy position.