...bowmen could be trained at once?
This question is quite common, so before other responses come, you might be interested in several responses related to the shift from bows to firearms.
This response detailing the history of the transition from neurobalistic weapons to early firearms from u/Valkine.
This response concerning the feasibility of the archery in the Napolenic era by u/hborrgg and u/Valkine
And another one by u/hborgg, this time focused on colonial times in North America.
This response related to the recurve bows on the battlefields by u/wotan_weevil
During the American Civil War, why were soldiers using rifles instead of bows and arrows? by u/SwampGentleman and u/rocketsocks
English Longbow: Is it true that the English Army fielded at Agincourt could have potentially defeated any army fielded at any battle anywhere, up until the invention of long-range rifles (mid 19th Century)? by u/nusensei
Bow and Arrow vs. Musket in the Revolutionary War by u/WritingPromptsAccy and u/hborrgg
My short overview of the physiological issues making bows a more or less technological dead end.