I think the apparent lack of strategy is largely due to both sides trying to keep up appearances. The really bad stuff Overhaul’s group is doing goes on in the underground complex which is probably where most of the security measures are. Plus the entrances/exits are probably hidden and apparently the place is a huge maze, so they probably thought it was reasonably secure (would be if Nighteye hadn’t been able to use his Foresight ability, even then they only know a fraction of what’s down there). As it stands, they intend to have their main enforcers hold off the police/heroes while they destroy any evidence and escape with Eri. Though the excuse that the enforcers were acting on their own and not following orders seems implausible.
On the police/heroes side of things, while they’re aware Overhaul’s group are criminals, they still need to do things by the book. The League of Villains are more like terrorists, so if they can connect them to Overhaul’s group they can probably forego a lot of the procedures. Also if they can find evidence of what they suspect is going on with Eri, they could at least take her into protective custody, which would seem to put an end to his biggest plans. One thing that didn’t seem right to me is that Nighteye is apparently pretty famous (has his own agency & a former sidekick of Allmight). You’d think the guy taking care of Eri would recognize him, even if the nature of his quirk isn’t public.
On an unrelated note, I actually liked the brief interaction between Midoriya, Iida & Todoroki. Considering everything the three of them went through related to the Stain incident, it makes sense they would have a special empathy for what Midoriya’s going through at the moment.