Speaking of Colt, they had a top strap design known as the Roots (or sidehammer) pistol in .28 and .31 caliber in 1855.
This was a smaller gun and it was not without it's problems.
The problems had nothing to do with the top strap, but were caused by the inner workings of the pistol.
Because of the great success of the 1851 Colt, when Colt designed the 1860 Army and 1861 Navy, they kept the strapless frame design.
With the popularity of cartridges after the War, Colt continued to make the top strapless guns until 1872, but they were chambered for .38 and .44 Rimfire cartridges.
The introduction of the 1873 Colt Army Revolver seems to have sealed the end of the strapless design.
Several other guns besides Remington used the top strap design.