Yes, the University of Texas has to balance public obligation with academic excellence. It's also in a constant battle with the State legislature to be more selective with admissions.
The fact that you think admissions rates are the only thing to measure a university by is your issue, not the university's. In fact, given the local government where UT exists, it's arguable that the University of Texas is pretty much as great an academic institution as it could possibly be given its mission and scope. Let's look at some specific colleges where automatic admission students don't tend to go. And we'll use USNWR because every system has its flaws but you like that one because you think it suits your argument.
Engineering - #11 in the United States. Some schools Texas is ahead of - Cornell, UCLA, Princeton, Penn, Northwestern, Duke, Wisconsin, etc.
Business - #19 in the United States. Florida, Rice, Notre Dame, Vanderbilt, etc.
Nursing - #24 in the United States. Penn State, Boston College, UC-Davis, Miami, etc.
Computer Science - #10. Cal Tech (!!!), Michigan, Columbia, UCLA, Wisconsin, Harvard, UC-San Diego, Penn, Purdue, Rice, etc.
Mathematics - #14. Duke, Penn, Wisconsin, UC-San Diego, Illinois, Northwestern, Georgia Tech, Purdue, Rice, etc.
I could go on. The University of Texas is an outstanding academic institution. The fact that there are thousands of auto-admits walking around the Liberal Arts buildings does nothing to change that, and in fact is a positive when analyzing the University's performance. UT has an obligation to help advance the interests of education in the State of Texas. Allowing those who started from a lower rung of society to experience college and get a degree is immeasurably important. Those children of high school dropouts eventually have children themselves and they teach the value of education to those future Texans.
In short, you're wrong in almost every way that you could possibly be wrong.