So assuming this is still Worm and Skitter?
Well first I have to take into account the Unspoken rules. Since right now, the PRT and the Protectorate is extremely weakened and divided in the aftermath of Edchina. I have to consider if we could take the hit that breaking the secret identity rule would cause to the Endbringer Battles and wheter or not taking out Skitter and only Skitter like this is worthwhile.
Now, on one hand, this could be the PR boost we need to restore confidence among the public both locally and nationally, a show of strenght and confidence, unite some factions within the organisation, booster recruitment in the future and potentially allow us to take back this city with the Criminal faction left leaderless, if we move quick enough and powerful enough that the locals who do support them end up not mattering.
On the other hand, I have to remember a few important facts. One, the Undersiders enjoy relatively large support among the locals, so moving to take them out could run into opposition, which could become disastrous if my attempt at capturing her ends up in a situation where my forces are seen opposed to the civilian population. Two, even without Skitter the Undersiders are a veteran group of villains with some very scary powers and they could do a lot of damage in retaliation. Grue can turn off all communications in the city and out of the city, Regent can take over people's bodies and considering how long he's had his own territory he likely has a number of patsies he could use for some very nasty shit which could not only hurt us, but with some smart planning on their parts turn the public against us. Bitch's dogs are basically walking tanks that are superbly agile, but while they can hit very hard they are actually the least dangerous things in this situation. No, the most dangerous one is Tattletale, who potentially has a mountain full of blackmail info that she could use to utterly ruin us, that's not counting the one fact that every Undersider knows, the identity of the Ex-Director. If that were to go out, then we would take irreparable damages. Beyond that, if we break the rule on secret identities, well she'll break them, not only painting big targets behind our heroes's backs, but also making future recruitment to be an utter bitch.
That's also not taking into account that the respect secret identity rules is crucial to the Endbringer defense. By using her secret identity, I would be telling all the villains that I would just catch them and fuck the truce. Meaning that they wouldnt help. Not only would that result in far more deaths and destruction among normals, but my own Capes are going to be bleed dry which further weakens us.
All in all, it seems that a direct confrontation is very much not only supoptimal, but also very much not worth it. Especially when in a school full of teenagers, thus full of cameras, witnesses and also potential collateral. Now in Tagg's defense, he is a military man, so I assume that he was aware of all of this. Otherwise he'd be stupid. So he was likely manipulated by Dinah and since she is the most powerful thinker precog, I would probably listen to her advice. Then again, we don't know for sure what kind of questions he asked her and how he asked her, and again how she responded the questions. So it's possible that a man who is less rash with a less militant background could have seen the trap and avoided it.
That would be my primary criticism of him. He acted too rashly and while Dinah did manipulate him, it is very possible, considering what we know of her powers and his personality that her answers led to him assuming things. So a much more subtle sort of manipulation that only made him want to do what he was already doing to do. In which case, maybe he just didn't care about the consequences, was more focused on the battle than the war. Anyways he had Skitter's identity, meaning that he now had leverage over her, that's something that he could have kept in his pocket and reserved for a more appropriate situation. Or used to directly or discreetly contact her, and thus forcing her to the negotiating table, proving both that I do have leverage, but also that I am perfectly willing to talk and not be stupid.
Risky? Certainly, but by questioning the Wards and the local PRT, and Dragon and Defiant, I could probably tell that she would be willing to talk. And this has less chances of going wrong and hurting the entire organisation than just brute forcing the issue.