1. The screens only show information that they could have already found out.
Notice how often a Starfleet crew member is able to tell us what the other ship is doing (raising shields, powering weapons, ...). It stands to reason that all other ships (of equal technological quality) have scanners on board to scan other ships.
I don't think there's that much to be hidden about the state of the ship itself, the scanners would already answer most questions.
However, the intentions of the crew are tactically important knowledge, but this is not shown on any screen.
2. Starfleet is peaceful.
The point of opening a communication line is to communicate with the other ship's commander. If we're focusing on ships that have been assumed to be hostile (at the very least up until the communication line is opened), then talking to them is tactically relevant:
- You can assess their behavior. Are they enraged, or are they simply apprehensive of you? Did you offend them in some unexpected way? Are they able to be talked down? Do they look willing to follow through on their threats?
- You can try to defuse the situation. Maybe it's a misunderstanding. Maybe the other ship is at war with an enemy whose ships resemble those of Starfleet. Maybe you did something that offends them, but you're culturally oblivious to. Maybe they are always this guarded about any race, and they're not behaving particularly hostile towards you (it just seems that way). Maybe you've stumbled on an important ship where any passerby would be treated as a potential danger.
- You can humanize yourself. If the other ship is already acting hostile towards you, and you wish for a peaceful resolution, it doesn't hurt to remind them that you are not military, a peaceful civilian crew.
Part of coming across as peaceful means lowering your defenses. Not to a point of recklessness, but at least to a point of not making the other party feel threatened by you.
Open communication, without hiding anything (e.g. the monitors), quickly conveys the message that you are not hiding anything and that you are not intent on combat.
If you hide tactical information, then the other party can possibly infer that you're scheming against them. Because if you truly had peaceful intentions, why are you hiding information that would be vital for combat? It sends the wrong message.