First, ESPNs expenses to the LHN are not limited to their rights fee of $15-$20M annually. They are incurring annual operating expenses to run the LHN. Do you know what those fees are? They could easily exceed $15-$20M annually. In business it all comes down to profit. So far the LHN is not profitable for ESPN, if it continues to not be profitable, ESPN will buyout Texas. You need to remember, ESPN is owned by Disney and in the end they are all accountable to shareholders. Disney isn't interested in losing money.
As far as Texas' brand. In 2010 it was probably worth ESPN creating the LHN, but today the Texas brand is diminished. Texas is still very powerful, but lackluster FB and MBB teams over the last 5 years has decreased their national interest. If I am given a choice to watch Texas, Alabama, Notre Dame, Oklahoma, Ohio State, Michigan, Stanford, etc on any given Saturday- Texas wouldn't be in my top 10. None of those schools have a LHN.
In answer to your question why would Texas take less than the annual rights payments stipulated in their contract. If you are familiar with Finance you would understand the time value of money. If I am owed $175M in total annual payments over the next 10 years, I may befinancially equal to take $140M today. I can then turn around and invest the $140M or use it to pay off debts.
Same concept as being a lottery winner. The person who recently won $475, could take the entire $475 over 30 years OR take $330M today. Taking the $330M today isn't taking less, because if they invest it and earn 2.73% on their money, they will breakeven.