Why does Texas have "Welcome To Texas" sign in Texas border ? But "Welcome to Virginia" or "Welcome to Washington" or "Welcome to Maryland" signs aren't there?
I dispute the premise of your question. (All images from a google Image Search for "Welcome to [State Name]")
You can find examples for all 50 states at this site - note however that while all 50 states are represented, that list is far from exhaustive of all the designs and styles that can be found, depending upon which border crossing you're at. Many states will, for example, have much more elaborate signs at the state border along interstate highways, and simpler, less imposing ones on less substantial roadways with lower traffic.