I know that this sounds like a stupid question but here me out. Surely something like a phalanx shield would've been very useful during battle. The ammunition at the time probably wouldn't have been powerful enough to pierce hardwood and they also could've been used as makeshift cover in an open field. When you look at historical paintings of 'The Napoleonic Wars' or 'The American Revolution' the soldiers just look like sitting ducks waiting for their turn to get shot and since soldiers didn't have to wear plate armour anymore then surely they could carry a shield of some sort.
Is there some battle that proved that shields were a hinderance and cost an army a battle? Or is it just a weight/resources thing?
One of the advantages of very early firearms over contemporary weapons such as bows and crossbows was that they were able to reliably pierce amour and shields. These "gonnes" used relatively poor quality powder compared with later muskets but a larger caliber would allow for the necessary penetration. There are certainly stories of wooden shields stopping firearms but these tend to be in the context of spent balls (i.e. outside of effective range) or very poor quality firearms.
In the 18th and early 19th century armour was largely ineffective, and while some was worn by e.g. cuirassier regiments it was only proof against pistol balls and sword cuts.
So why am I talking about armour when the question was about shields? Simply because if a steel cuirass cannot stop a projectile, a shield will not be able to either. Because a cuirass is worn close to the body, the weight is distributed relatively evenly and so can be heavier (and therefore more effective) than a shield which is carried in the hand.
Any shield heavy enough to stop a musket ball would severely limit the mobility of the user to the point that they would not be able to perform their task on the battlefield. If you don't need to move it is more effective to take entrenching equipment and construct field defenses that can protect against cannon as well as muskets.
In addition to the other posts here, I'd like to direct you to an article in the Journal of Conflict Archaeology, in which the researchers conducted an experiment to test how much protection a shield provided the user at 150 yards.
ROBERTS, BROWN, HAMMETT AND KINGSTON, "A DETAILED STUDY OF THE EFFECTIVENESS AND CAPABILITIES OF 18TH CENTURY MUSKETRY ON THE BATTLEFIELD" Journal of Conflict Archaeology, 4(1-2), 1-22.
I would like to chime in to add something to the previous answers, because while armor fell out of use because of the influence of firearms, this process took a relatively long time of around 150 years, from the 16th century when arquebuses started spreading around the battlefield to the mid to late 17th when they had become the dominant infantry weapon, and this period did see extensive use of armor by cavalry and heavy infantry, both because it was still useful against blunt weapons and because shotproof armor did exist, but it was terribly heavy as well as expensive, and yet was still vulnerable to muskets, larger arquebuses developed specifically to counter this heavier armor, so the cost benefit analysis became eventually unfavorable to the usage of armor.
But the important thing for the question is that during this period, shields did exist! but basically as a tactical dead end that perfectly exemplifies what i wrote above. In the early age of the pike and shot a third component that is often overlooked existed, the sword and buckler man, equipped with said weapons, were used to take advantage of the unwieldy nature of pikes in close quarter combat with their shorter swords as two enemy formations clashed, and they were also used to defend commanders and ensigns. Men armed with shotproof bucklers existed, and who knows, they might have saved a few soldiers' lives, but predictably they were very heavy and thus unpopular, because of course carrying around a buckler with the strength of a single arm meant that the weight must have been a huge limitation. So lighter bucklers were preferred anyways, and eventually the bucklermen altogether would fall out of use, as well as other weapons like halberds or bills, in favor of heavy infantry solely composed of pikemen.
In the 18th and 19th centuries soldiers might look like sitting ducks, but quite frankly how else can they look? The late musket era of war is absolutely saturated by firepower, from several sizes of field artillery firing solid cannonballs, explosive shells and grapeshot, to riflemen picking off officers, drummers and soldiers well outside effective counterfire range, to even rockets copied from those in India, and of course the enemy infantry which is 100% composed of musketeers, and indeed there's no cost effective form of protecting yourself from any of this, so it's a very nerve wrecking situation but there's not really much soldiers can do but fire away at the enemy and hope that none of those invisible bullets flying by hit them, or arm themselves with the courage to charge at the enemy with their bayonets and then hope that the enemy spirit breaks before their own does.
