Flatbush_Fi, the short answer is that door-holding delays are rarely just one operator. When a train at a high-transfer station like 14th St/8th Avenue misses its scheduled departure, the line supervisor will sometimes hold the train behind it at the previous interlocking to keep spacing. That means the operator at 14th isn't just dealing with their own car, they're inheriting platform overcrowding that built up while the previous train was late.
I used to ride the E from Jackson Heights and you could see the same cascade at Queens Plaza: one train goes slow because someone's arm is in the door, the next train arrives fully packed, the conductor gets more aggressive with announcements, and then people start blocking the doors intentionally because they can't fit. It becomes a loop.
The full manual announcement is allowed under the rulebook if the conductor determines conditions require it. I've heard it more in the last two years, especially during the 5-6 p.m. peak. But I don't think it's a new written directive. It's more that crews are being told at the terminal to keep the line moving, and the announcement is the only tool they have when the train is already full and there are still 50 people on the platform. The actual dwell-time problem is unsolvable without running more service, which costs money and crews they don't have. So you get the PSA and a lot of people staring at each other.
One thing I've noticed: if you see a conductor doing the full announcement, that train is probably going to be held at the next interlocking to let the one behind it pass. So even if you get out of the station, you might still lose another minute at the signal. That's the part that drives me nuts.