Tsukiyumi wrote:As I said, the Republic of Texas
joined the US. The California Territory was turned
into a state.
But there was a short-lived
Californian republic which was proclaimed by American settlers, and lasted for a few weeks before being annexed by the US. (Likewise, Hawaii existed as an independent kingdom before being conquered by US interests.) But even disregarding that, Texas wasn't the only place to go directly from nationhood to statehood:
Vermont existed as an independent republic from 1777-1791, before choosing to join the US.
Anyways, how could a colony become a member? No matter how prosperous it is, it's still just a colony. Unless it declares it's independence, and later chooses to join, or if it was always independent, and grows powerful enough to be accepted as a member.
In the case of the British dominions like Canada and Australia, they did have a rather gradual evolution from colonies (mid to late 19th century) to nearly independent countries (late 19th, early 20th century) to fully independent countries (modern day), without an explicit declaration of independence.