In my case, at a "startup" (it isn't) I was offered the non-compete, with extremely nasty and broad language that unfortunately is enforceable in Texas, 3 months after I had been working there. You can imagine the coercive effect of that one: sign this or look like you got fired at 3 months. I was able to negotiate some changes to the broad clauses, which by their own admission were cut-and-pasted from somewhere else, but it made for an appalling experience.
Which may explain why the unemployment rate is so low in Texas. Anybody who already lives there is employed if they want to be, and are employable. Texas has trouble attracting talent from outside of the state for the reason you mentioned, and the backward labor laws in the state.