Please look at this post that I and /u/elos_ did previously on the matter of linear warfare. However the picture you linked is from the Franco-Prussian War which I would recommend /u/elos_ to discuss.

Overall, there was purpose and reason, going prone means you can't reload and worse, you can't maximize accuracy.

It's important to remember that (like any period) there are complexities to warfare that don't make it into the popular imagination.

Since you're tacitly describing a popular notion of Napoleonic era warfare, I should add that there were in fact significant forces available to commanders in the age of the musket that utilised cover, concealment and didn't just line up in pretty formations. I'm best suited in knowledge around the British Army's regimental system, so I'll contribute from that context.

The British Army started employing riflemen by equipping a 5th Battalion to add to the existing 4 battalions of 62nd Foot (Royal Americans) in 1797. One battalion does not a significant capability make, but by 1800 a "corps" of skirmishing riflemen was specifically raised precisely to operate under cover, in open order, and somewhat independently. Notably differences to line or heavy infantry included green uniforms (rather than red), 21-inch "sword" bayonets and Baker Rifles instead of the typically used Brown Bess musket. These men would later become the 95th Regiment of Foot, better known as the 95th Rifles approximately two years later.

Individuals also occasionally defied our popular notions of linear combat. During a confrontation at Cacabellos during the Peninsula War, a private soldier by the name of Plunket (a soldier in the 95th as it happened) successfully demonstrated a near-prone firing position by which the rifle was supported on the outstretched feet. The firing position was promptly named after him.

Others have posted about Linear warfare - my only addition here would be that Richard Holmes' otherwise well regarded (if popular history) work does mention accuracy rates for smoothbore musket fire which very much support the case for en-masse volley fire to deal sufficient shock to a formed body to stop it's forward momentum and perhaps soften it up prior to closing with it - the idea being that it was the only way infantry would substantially hit anything. Whilst it might seem ridiculous in hindsight, given the technology at the time it was still one of the primary means of maximizing the combat effect of a formed unit.

The other posters have already covered it pretty well. And while the social factors and ability to keep soldiers under control were major factors, it helps to think in terms of commanding very large forces. Dense formations have been around long before blackpowder firearms have, if a general has an army of 10,000s of men and he doesn't want the enemy to face them piecemeal then he needs to pack them in shoulder to shoulder and fit as many on the front line as possible. When muskets were introduced their slow rate of fire and relatively poor accuracy meant that whoever could put the most bullets in the air at once easily gained fire superiority, so it continued to be important to fit as many men into the front lines as possible. Even if a sniper did start shooting from cover they generally weren't going to do much damage until your troops replied.

Linear formations started to phase out with the advent of rifles, breechloaders, and finally machine-guns and improved artillery meant that a small group of men could easily slaughter dozens out in the open within seconds.