This stood out to me because a decent part of our success against Britain during the revolution was because of hit and run tactics.

This is largely a misconception. While the US milita did occasionally use "guerrilla" tactics (Guerrilla warfare wasnt a thing until the French Campaigns in Spain during the Napoleonic Wars, so on that level the Americans couldnt practice guerrilla warfare) such as hit and run attacks, and the use of loose formations and cover (skirmisher tactics), most major actions fought in the AR followed traditional European tactics. This is especially true of the George Washington's Campaigns. Most Revolutionary battles were fought using the linear tactics (men in a line firing mass volleys).

But it gets confusing, because when people talk about George Washington's general strategy, he actually did emphasize a strategy of delay and "hit and run" battles. Washington did an good job keeping the American army out of serious action, and instead focused on attacking isolated British detachments, and then fleeing before the main force could intervene in the battle. But where these armies met, they fought in the tried and true linear style.

But the AR armies (both the British and the Americans) incorporated units which fought "Indian style", or using skirmisher/light infantry tactics. These units did abandon the line, and usually took advantage of the available terrain and cover to attack the enemy. They even used rifles, to improve accuracy and deal more precise damage to the enemy. But these troops didnt form the great majority of troops on either side. They were useful in difficult terrain (like forests, rocky places, ect.) where they could attack a disorganized enemy, or attacking the enemy's flanks and rear. But against a disciplined and determined enemy, light infantry didnt have the power to hold off the enemy, and a strong volley (which they British were capable of delivering) could wreck even a loose skirmisher formation. They were useful, but tactics in the 18th century could not operate with light infantry alone.

As to how the American Army maintained these tactics into the American Civil War, we have our friend Winfield Scott to thank for that. After the War of 1812, Scott imported training manuals and strategic treatise from Europe, including the works of the Baron Jomini. These manuals all dictated the same linear formations which the Americans had used in the AR. By 1861, the US Army had developed a strong sense of European tactics and strategy, and the Armies of both sides really fought using the best, most modern European tactics. The ACW was an extremely modern war, even if we look back and say "look at those dummies, they are making it hard on themselves!"

It seems like those tactics would rely on having more soldiers firing more bullets.

Thats actually partially correct numbers always counts for a lot in military science. But actually, Robert E Lee won a classic victory at Chancellorsville, which was the embodyment of current European (and American) thinking on how a battle should be fought, both tactically and operationally. And Lee did this outnumbered over 2:1.

That 3:1 number is the ratio of the populations between the Northern and Southern Populations, which is indicative of the great materiel difference between the two "states". It helps illustrate the effectiveness of the Union strategy of attrition and asphyxiation of the CSA. We could get into that too, if youd like.

I hope all of this makes sense and isnt too confusing. Basically, Light Infantry tactics are effective at harassing the enemy, disrupting them before the main event, and sapping the overall strength. And it can be devastating under the right set of conditions. But its a very situational tactics, which could not (and Light infantry tactics today can not) compete with the Linear tactics when the Linear forces are on their strong ground, and especially when the linear forces use Combined Arms (Infantry, Artillery, and Cavalry).