Why transformerless power supply need a capacitor to decrease the current?
How confident are you that your rectified mains voltage will be exactly 310V?  

How confident are you that 100 LEDs in series will have a voltage drop of exactly 310V?
Have you read the datasheet? What is the Forward Voltage tolerance specification?  

What if your mains is actually 315V and/or your string of LEDs adds up to 308V?  

LEDs need current limiting - they are not voltage-driven devices.