Because the LTC holder is under no obligation to show it outside of when ID is demanded by a law enforcement officer.
Think of how this law can be abused. Currently, there is no way the public can get a record of all the LTCs in the state of Texas. If a school district really wanted to, they could submit the name of each person who could come in contact with a student, claiming they wanted to know if they had a legitimate LTC. DPS must then respond with a yes or no for each name and voila, the school district has a list of ALL the parents/relatives/friends/neighbors/TEACHERS who have an LTC. There is nothing preventing them from releasing that information to the public, unlike DPS.
Additionally, Texas is an at will state... no reason they can't just let teachers with LTCs go. After all it is, "for the safety of the children".