Problem using Serial Monitor with ATmega32U4-based boards

[technoblogy]

With an Arduino Micro or a LilyPad Arduino USB the serial hangs up if I try to paste a block of text into the Serial Monitor Send field with more than about 384 characters. This doesn't happen on other boards, such as the Arduino Uno, Arduino Mega 2560, or Arduino Nano.

I can reproduce this effect using the following simple test program, which echoes the text and prints the number of characters every 64 characters:

void setup()
{
  Serial.begin(9600);

  while (!Serial);
  Serial.println("Ready");
}

int count = 0;

void loop()
{
  if (count % 64 == 0)
  {
    Serial.println();
    Serial.print(count);
    Serial.write(' ');
  }
  while (!Serial.available());
  Serial.write(Serial.read());
  count++;
}

My setup is: Arduino IDE 1.8.2 on a MacBook Pro running Mac OS X 10.11.6.