Part of the reason that the US government only ordered 1,730 Henry rifles was because they judged the New Haven Arms Company unable to scale up their production of c.200 weapons per month sufficiently quickly.The Henry Rifle-14 shot metallic .44 caliber rimfire cartridges is in production before the Civil War began ... so with sufficient orders they could have scaled up far faster than most.
The US government ordered 700 Spencers for the Navy in July 1861 and 10,000 for the Army in December 1861. Spencer misses his deadline of starting deliveries by March 1862, leading the government to reduce the order to 7,500; it takes him until December 1862 to produce 1,200 weapons and June 1863 to fulfil the order of 7,500.Christopher Spencer's 7 shot rifle/carbine drew on his experiences as a Colt subcontractor so he'd also seen how to scale up to tens of thousands in production
Burnside was due to deliver his first Spencers in November 1864, a deadline which he misses: he makes his first delivery on 15 April 1865.the design was simple enough that Ambrose Burnside's carbine factory was quickly able to retool to produce Spencers
In June 1861, Ripley orders 3,000 carbines from Sharps. The first weapons are delivered in September 1861; by the end of the year, Sharps has delivered 5,800 carbines and 100 rifles.The Sharps (an 1848 design based on the 1819 Hall Breechloader Rifle made at Harpers Ferry Arsenal in Virginia where Christian Sharps trained) was easily being converted to .50-70 metallic cartridges
What I hope all of the above shows very clearly is that there simply wasn't the industrial capacity to produce large number of breech-loaders in the early years of the war. If the contracts placed, which some have deemed hesitant and inadequate, can't be met, how could it realistically be expected that large volumes of additional weapons could be made? Furthermore, all those arms bought on the European market- not to mention all the percussion muskets in the Federal and state arsenals- would have been unusable. The only real answer to "what does an American Civil War fought with cartridge rifles look like" is "very small".
Most early breech-loaders focus on combustible cartridges. In the mid-to-late 1850s Britain experiments with a number of breech-loading cavalry carbines (the Leetch, Sharps, Greene, Terry and Westley Richards), and all of them use a paper cartridge. When they trialled breech-loaders in 1864 only two of the eight weapons had metallic cartridges, one of which was the Snider.one thing I'm curious about... what was the rest of the world doing with cartridge firearms at this time?