In my prosecutor days, I got volunteered to advise the tac team and the school resource officers on this, mainly because I had a military background, my father was a school administrator, and I am a gun nut. Their policy, written by a civil lawyer, said "may" and not "shall." Policies like this are rarely written by lawyers using "shall," because they do not account for variances in the situation. In other words, if the policy says "shall enter," and the officer observes an IED, the "shall" policy will do more harm than good. "Shall" does not allow for discretion, which may save live.
That said, I cannot help but wonder how any of these Texas cops can live with themselves. The shame of cowardice is hard to live with.
As an aside, the local policy was that the first pair of responding officers on scene "may" form an entry team and make entry. No need to wait for brass permission. And I have no doubt they would go.