Regarding parallel mode 16x2 LCD using HD44780
It's less popular since that LCD will requires minimum of 6 data pins (in 4-bit mode) or 10 pins (in 8-bit mode.) Then you'll have to add power, backlight power, and contrast adjust.
This is why people are adding that I2C daughter card (usually $2 or less) to save the extra effort.
See Arduino flavor of using parallel mode: https://www.arduino.cc/en/Tutorial/HelloWorld