It's a basic tradeoff of firepower for protection. Sure, an equivalent weight ship would be able to carry more guns if it didn't have the armor, but when you can armor a ship enough that conventional naval gunnery is going to have little effect, the tradeoff absolutely becomes worth it.

It's hard to overstate just how important armor was becoming for warships at that time. About a decade before the US Civil War, the vulnerability of traditional wood-hulled ships to exploding shell fire was demonstrated against the Ottoman fleet at the Battle of Sinop. During that same war, the British and French experimented with armored floating batteries - the precursor to ironclads - and found that they were fairly resilient against gunfire. So, several years before the US Civil War, the importance of armoring ships was clearly demonstrated. In fact, the British and French both had begun work on ironclads before the Civil War even broke out - the French launched Gloire in 1859, and the British followed a year later with HMS Warrior.

Unlike the littoral ironclads of the US Civil War that dominate the popular perception of ironclad ships, both Gloire and Warrior were traditional designs. However, the limitations of that arrangement were quickly becoming apparent. Armor was heavy, and Warrior left the ends of the ship unarmored to save weight. Both Gloire and Warrior also carried fewer guns for their weight - Gloire with only 36 guns to the contemporary wood-hulled Napoleon's 90 guns of similar size. Warrior carried 40 guns that were generally larger and more effective than those on older ships of the line, but Warrior was itself a massive ship at almost 10,000 tons (compared to Napoleon's 5,100).

The result of this early ironclad development, as well as the experience in the Civil War, was that navies were finding armor would outperform contemporary guns and that fewer heavier guns would have to be the tradeoff to attain effective firepower. This evolution took a few shapes. Some navies stuck to Warrior's example, placing guns broadside in an armored citadel. Protection was limited to the central area of the ship where the guns were placed, protecting the ship's fighting capacity while limiting the weight of armor to improve seakeeping.

Central battery ships like that, however, still suffered from the inherent inefficiencies of a broadside arrangement - in effect, half of the ships guns were dead weight in a typical engagement. Providing a wide firing arc for guns would solve that issue by allowing fewer guns to provide similar firepower. Not surprisingly, this meant turrets quickly came into favor. Not all turretted ships shared the fully rotating armored compartment like Monitor had - the Confederates had famously ordered a ship (CSS Stonewall, later known as Kotetsu in Japanese service*)* that featured gun on a swivel mount in the bow that had several firing ports. This limited firing arcs to where the ports were, but it cut on weight and complexity by forgoing a revolving armored turret.

If that wasn't enough, ironclads proved durable enough to ramming to come back into fashion as a naval tactic. Experience at the Battle of Hampton Roads in the US and Battle of Lissa in the Adriatic appeared to demonstrate the effectiveness of ramming as a tactic by ironclads, so for a surprisingly long time ships were equipped with rams. Though it likely stuck around longer than reasonable, the tactic at times was quite effective - Peru's Huascar would ram and sink the Chilean corvette Esmerelda at Iquique in 1879 after its guns failed to score any hits. Huascar, meanwhile, was impervious to the fire from the wooden-hulled Esmerelda.

Effectively, over the second half of the 19th Century, naval guns and shells had advanced to leave traditional wood ships unacceptably vulnerable. Experience in the Crimean War and US Civil War demonstrated the extreme durability of ironclad vessels, but the weight of the armor required a tradeoff in firepower to ensure seaworthiness. Ship designs then evolved to be more efficient with their gunnery, relying on smaller numbers of larger guns, wider firing arcs, and eventually settling on revolving turrets that maximized firepower in any direction.