So Washington has another waste of a Lt. Gov. office like Minnesota. There's a small movement in the Minn. legislature to abolish the Lt. Gov. option and let the Sec of State be next in succession but for some reason no one seems to want to get behind it. This is despite the current Lt. Gov. being basically the most unpopular political figure in state besides Michele Bachmann possibly (in a nutshell she was also Sec of Transportation due to Lt. Gov. being a nothing job, and became the scapegoat for the bridge collapse. The Senate thus refused to reapprove her as Sec of Transportation.)
How many states have a Lt. Governor with any duties? The only ones I can think of are Alaska, Hawaii, and Utah, where the Lt. Governor basically does the job of the Secretary of State.
In Texas the Lt. Governor has more power than the Governor.
True, but even in Texas, the bully pulpit of being Governor and the possibility to raise public outcry and pressure on the legislature does help augment the admittedly absurdly-weak office of Governor. Also, the Governor's power to call the legislature into special session is a lot more relevant in most states: Texas has what might be the laziest legislature in the First World (certainly the laziest with such a large, important jurisdiction), and the words "special session" strike fear into their hearts.
I'm not disagreeing with you, I'm just saying that the Governor of Texas does have some real influence. The Lt. Governor is "the most powerful" official, but it's a very smoke-filled-back-room power.