The house to control members, obviously. Otherwise there is no point having or convening the house as they can be an unruly and uncontrolled mob out on the street just as well as they can in the uncontrolled house.
That tracks if you assume the House leadership is always right. But when an entity of any kind is perceived to be wrong and perceived to be abusing its power, people tend to rebel. That's what happened in the American Revolution and in many subsequent events when people took to the streets.
And it was not that bad in the Tennessee House case. Rules of decorum were violated, yes. The gallery was packed and unruly, yes. People were protesting in the streets and inside the capitol building, yes. But in fact, the House did not cease to function. In short order, the representatives were back in the chamber and conducting business.
There were no arrests, fires, property damage, injuries, fights or other such things. This was a loud and temporarily disruptive demonstration, not a riot, and not something that disrupted the House for long. Had it been a non-violent sit-in that kept the House from doing business, arrests would have happened. But there were no arrests because the House was not significantly disrupted for long.
I presume the speaker always had the power to clear the gallery of any and all people who were disrupting House proceedings. I know in Washington, it happens quite often that one or more people are disruptive in the gallery. When that happens, the committee or House or Senate members simply pause for a moment as officers remove the disruptive people at the order of the chair.
I don't know why TN House Speaker Cameron Sexton did not order the gallery cleared. It may be because the House was in recess the entire time the bullhorn protest went on, except for a very short time when the House was in session. I don't know. I do know he had the power to clear the gallery but he did not do so.