One reason the Texas legislature has always been so corrupt is that the anti-government founding fathers of Texas chose that approach. It meant that only the independently wealthy could afford to enter the Lege -- and that meant mostly cotton plantation owners and big cattle ranchers (at the time), with no representation of the poor former Mexicans who made up much of the state's population. If you set out to deliberately plan a system to keep the privileged in power, you couldn't come up with anything more effective. And that was the point.
Try reading Robert Caro's bio of LBJ, particularly vol. 1, "The Path to Power", which describes Johnson's boyhood years through his start in Texas politics. His father was a member of the Lege but not wealthy, and not amenable to bribery -- the usual formula was "beef, bourbon, and blondes", provided by influence-peddlers who wanted legislation that benefited their interests -- and he suffered for it, eventually going bankrupt and losing his farm. He could have avoided impoverishing his family if only he had been open to a little corruption, and LBJ evidently considered him a fool for sticking to his ideals. Not averse to a little corruption himself, LBJ became a millionaire through several businesses whose real ownership was hidden from public scrutiny.
No, starving the watchdogs doesn't work.