I own three .223 rifles and one 22 Hornet. The Hornet is fun to shoot and fun to hand-load. It fits a different category of hunting and shooting than the 223s.
By the way, the 5.6x35mm Vierling uses .222 cal bullets and NOT the 224 used in a 22 Hornet. Plus it is not exactly a 22 Hornet. It is a sort of cross between the OLD 22 Winchester Center Fire and the later 22 Hornet. Originally the 5.5x35mm was loaded with non-jacketed slugs. So you would not be buying a true Hornet and the rifling twist and bore diameter would not be a good idea warmer modern loads.
RCBS makes or used to make a sizing die to make 5.6x35mm Brass from 22 Hornet brass. It was $100 when I looked into the idea a couple years ago.
The .22 WCF - also known as the .22-13-45 Winchester Center Fire, of 1885, introduced for and with the Winchester-Browning single-shot rifle of that year. This is probably the longest-lived and most popular of the three pioneer .22 cartridges. It was chambered not only in the Winchester single-shot from 1885 to 1920 or later and reportedly in some late Model 1873 Winchesters but also in the Ballard Number Three gallery rifle in about 1886 to 1891 (where it cost a
dollar extra) and in the Remington-Hepburn Number Three rifle (1886 to 1906) and their fancy and rare Number Seven rollingblock rifle (1904 to 1906).
This cartridge also went to Europe, where it became known as the 5.6x35mm Rimmed Vierling, was loaded to higher velocities than the United States loads were (thirty-ninegrain bullets at 2,630 feet per second by RWS and forty-six-grain bullets at 2,030 feet per second by DWM), and reached considerable popularity as the kleinkaliberluuf cartridge for drillings & vierlings.