I lived in Houston most of my life. In 50 years of driving there, I have only used a toll road twice -- once was by accident, the second was on purpose to avoid an accident. I never bought a toll pass.
In Houston, driving the Interstates and toll roads is often the worst option to get where you want quickly. While it does take time to learn all of the side street options that will get you where you are going quicker, just stay off the highways -- especially in the Galleria area. There is no need for anyone, including tourists, to have to drive on a toll road to get anywhere.
Set your GPS to avoid tolls and drive happy.
If you have a rental car, those are all set to allow toll road driving, so don't worry if you end up on one. The fees charged by the rental companies can be high, but no where near the fine for not having a pass.