I have only one bike tour (Texas to New York) in my past, but here in Texas I definitely would carry a water filter (as I did to New York). Texas is a big state and very variable, but some of the arid Western counties are among the most sparsely populated real estate in the entire Lower 48 States. In these places you could pedal yourself out of reach of water , especially if, for whatever reason, the bike became inoperable.
OF COURSE the next people passing by would almost certainly stop to help if you needed it but if no one was passing by.....
Surface water is generally scarce to absent but cattle are not, and cattle must drink every day. I would bring a filter as emergency gear in case I ever found myself obliged get water from a stock tank.
But then I tend to be a "worse-case scenario preparedness" kind of guy, especially at the low cost of only a few extra ounces of gear.
Mike