You need UM/UIM insurance in Texas. it covers you, for any injury or damages that an Uninsured or Underinsured motorist causes to you, your vehicle, and your passengers. Before this recent influx, when I still had access to ISO data, based upon reported accidents 38% of the drivers and or vehicles were uninsured, in Texas. Now toss in all the non-reported accidents, and the drivers that have not been in an accident, yet. You most likely have a less then 50% chance the other driver has insurance, a valid license, a registered vehicle, or any way to pay for your damages.
That doesn't work the way you think it does. About 20 years ago my wife was in an accident (lady ran a stop sign and plowed into my wife). Cops came, gave the lady a ticket for no insurance, and my insurance would not pay the repairs for some reason. It was something I was unaware of, and don't recall all the details now.
But I was under the impression that if I paid for UM coverage I got my car fixed by insurance. That didn't happen.