A new set of pixels every 16ms is about throughput and we do have that. But the latency today is worse than in the VGA era.
If you have a completely black screen and want to draw a tiny white circle in the middle of it, it will take your processor or GPU less than a microsecond to change the bytes. Less than 16 milliseconds later (an average of 8ms, actually) the updated bytes will be flowing through the HDMI wires and into the monitor. There they will be stored into a local buffer. If there is a mismatch between the image format and the LCD panel then it will probably be copied to a second buffer. Some DMA hardware will then send the bytes to the drivers for the LCD and the light going through those pixels will change. All that can easily add up to 50ms or more.
If you have a completely black screen and want to draw a tiny white circle in the middle of it, it will take your processor or GPU less than a microsecond to change the bytes. Less than 16 milliseconds later (an average of 8ms, actually) the updated bytes will be flowing through the HDMI wires and into the monitor. There they will be stored into a local buffer. If there is a mismatch between the image format and the LCD panel then it will probably be copied to a second buffer. Some DMA hardware will then send the bytes to the drivers for the LCD and the light going through those pixels will change. All that can easily add up to 50ms or more.