There are many different reasons.
Reason #1, many calibers are, or were, named by their bore diameter. Now I realize that the groove diameter is often called the bore diameter on the internet, but that does not make it right. If, in your last example, you bore a half inch hole in a bar of steel, .500", and cut rifling grooves .005" deep, then you have a groove diameter and bullet diameter of .510". Most metric calibers are stated for bore diameter, like 7.62mm = .300" with .308" grooves and bullets. One maker calls his .300" bore rifle a 7.82mm for bullet diameter.
Reason #2, some calibers were named by their case diameter, usually because they had a heel bullet the same bearing surface diameter as the brass, and going down a barrel of that groove diameter. The .357 Magnum is based on the .38 Special, which was based on the .38 Government/Long Colt. The .38 LC with a case diameter of nearly .38" had a heel bullet of the same diameter, inherited itself from the conversion of percussion revolvers made for .376"+ balls. But then S&W went to inside lubricated bullets, the INSIDE diameter of the case, .358". They kept the case diameter and reduced the bullet and barrel. The big soft .38 LC bullets would swaged down safely, hence the early marking, ".38 Government and S&W Special."
Reason #3, two digits. Why try to remember .172 or .452 when you can just say "seventeen" or "forty-five"?
Reason #4, advertising. The .22 centerfires were standardized at .224" groove and bullet diameter pretty early on. But you have to identify your product, so .218 Bee, .219 Zipper, .220 Swift, .221 Fireball, .222 Remington, .223 Remington, .224 Weatherby, and .225 Winchester ALL take .224" bullets. But .22 Hornet (early), .22 Remington Jet, and .22 Savage High Power do not. The Hornet and High Power are older than the .224" convention and the .22 Jet was designed to shoot with either the centerfire or a .22 long rifle conversion insert or spare cylinder.