If the room calls answers out and the remote half types them, you have rebuilt the two tiers with extra steps. Everyone answers in the same place, including the student sitting two metres from you.
A shared screen reaches remote attendees late, small, or not at all if they are on a phone. Saying what the numbers show costs ten seconds and is the only version everyone gets.
The count against the number of people connected is your attendance signal for a group you cannot see. A count that slides between the second question and the fourth is worth stopping for; the answers themselves will not tell you that.
Otherwise the room hears only your answer and the person who asked has no way of knowing they were heard. Reading it out also stops you smoothing it into the question you would rather have been asked.
Remote attendees compose the real question once nobody is looking at them, which is usually several minutes after the moment they would have raised a hand. Something that is still open when they get there catches it.