I've covered the topic of bows in the musket era in this video.

The impact of bows is greatly overstated. While there are some exceptional cases where well-trained archers faced off against low-quality musketmen, guns were superior to bows, and every culture that could readily access guns switched to them. I find Donald Featherstone's summary best: the gun is a perfectible weapon (The Bowmen of England). The gun could be and continued to be improved, and its function was tied to it development. The performance of the bow was locked to its user.

First, let's knock out some misconceptions.

"More deadly" is a vague qualifier. If anything, arrows were less deadly. The puncture wounds caused by arrows seldom caused immediately lethal wounds. Few battlefield skeletons show fatal wounds by arrows. In contrast, a musket ball created far more devastating wounds, shattering bone and creating large wound channels.

"Faster firing" is true on paper, but has very limited application in real battle. Sources tend to overstate the firing rate of a bowman, but a realistic figure proposed by Mike Loades in War Bows sets it at around 6-8 shots per minute. When tested by Mark Stretton, one of the leading war bow shooters with a 130lb bow, he barely managed 10 shots in one minute, but he was totally spent by the last shot and could definitely not do 20 shots in 2 minutes. The physical effort required to shoot a bow that heavy with that speed does not compared to the steady 3-4 shots per minute a typical musketman could do consistently.

"More accurate" is also overblown because of the different scales used. "Long range" for a bow is in the 100-200m range, but accurate point shooting is really only possible under 50m, when the archer is shooting directly at the target (the "point on" on "point blank" distance). Beyond 100m and it's less accurate, indirect area shooting. Muskets are actually far more accurate over a much longer range, but they were typically used in shorter distance because of doctrine and volume of fire.

In an account by the French general Marbot, serving under Napoleon, his army skirmished with Baskir horse archers. His journal mocks the Baskirs:

"During our stay on the plateau of Pilnitz, the enemy, and above all the Russians, received many reinforcements, the main one, led by General Benningsen was of not less than 60,000 men, and was composed of the corps of Doctoroff and Tolsto and the reserve of Prince Labanoff. This reserve came from beyond Moscow and included in its ranks a large number of Tartars and Baskirs, armed only with bows and arrows.

I have never understood with what aim the Russian government brought from so far and at such great expense these masses of irregular cavalry, who having neither sabres nor lances nor any kind of firearm, were unable to stand up against trained soldiers, and served only to strip the countryside and starve the regular forces, which alone were capable of resisting a European enemy. Our soldiers were not in the least alarmed at the sight of these semi-barbarous Asiatics, whom they nicknamed cupids, because of their bows and arrows.

Nevertheless, these newcomers, who did not yet know the French, had been so indoctrinated by their leaders, almost as ignorant as themselves, that they expected to see us take flight at their approach; and so they could not wait to attack us. From the very day of their arrival in sight of our troops they launched themselves in swarms against them, but having been everywhere repulsed by gunfire, the Baskirs left a great number of dead on the ground.

...I had these [prisoners] brought to the Emperor, who, after examining them expressed his surprise at the spectacle of these wretched horsemen who were sent, with no other arms than bows and arrows, to fight European soldiers armed with sabres, lances, guns, and pistols!…"

He cites that despite shooting volleys at his infantry, only 1 in 10 arrows in their mark. Ironically, Marbot himself was hit in the thigh, though he made a full recovery.

The key point in this discussion is the notion that archery has to be brought back, which raises the following problems:

1. Training. The expertise in using bows in warfare had long expired. It had been several generations since bows were commonly used in warfare, so the skill in the use of bows was almost lost. It's worth noting that this is the entire basis of Gao Ying's Way of Archery manual written in the 15th century, where the Ming armies were making more use of firearms over bows. It took many years to become proficient with a bow, but a musketman could be trained to be effective in months.
2. Supply. Firearms was an industrial production line. The military industrial complex can mass produce firearms and ammunition. Bows and arrows were always an artisian craft, in the hands of few experts producing low quantities of bows and arrows. During the medieval prime of English archers, England had to import most of its wood from Spain and Italy. The archers at Crecy and Agincourt were said to have around half a million arrows on campaign. That scale of production, alongside firearms, was an unrealistic investment.
3. Effectiveness. As said above, a bow is only as effective as its user. Fatigue and disease cripples the archer, resulting in less accurate shooting and weaker shots as the battle goes on. A musketman can continue to function as long as his weapon functions and he has two hands. The conditions of battle must also be unrealisticalluy ideal for archers: wind and rain largely negate the effectiveness of bows and arrows, and in a modern battlefield, the smoke will obscure their targets.
4. Purpose. Archers had a unique specialist role in medieval warfare: they functioned as the artillery of the army, providing long-range shooting to disrupt and entice the opponent into battle. By the gunpowder era, this role was replaced by... artillery. Ultimately, why invest in training a corps of archers when you have the king of battle?

Overall, bows were largely a historical exoticism even by the time of gunpowder armies. People like Benjamin Franklin would bemoan the lack of bows, but their claims were as fantastical as a modern day armchair historian doing fantasy battles, overstating their effectiveness and speed. The reality is that bows no longer had a function on the battlefield, even though the circumstances (densely packed unarmoured infantry) would have been ideal targets. A unit of archers would be wiped out by the first artillery barrage or the first volley of muskets.