Do I really need to press on “Eject” when taking out my USB Drives? And why?

YES you need to Eject the USB drive before removing because it may cause to corrupt the data on USB and prompt you for formatting your USB before using again.

Yes, that is proper method of removing USB and it helps in avoiding the data corruption and USB will not have any bad sectors and your USB operations like copying data, reading data from USB and wrting data (ex copy of files,docs,pdf's )won't crash.

you should probably always eject a drive before removing it, even if the context menu doesn't have an eject option. cause sometimes flash damage or files interrupt, even you complete your transfer data, some main sys. files still ready to get or give the date . 

Dear,

After greeting, thanks for the invitation. Your question can be answered in two ways:

-If your are using MAC devices it will ask you each time you unplug the flash drive as it cashes every single portable devices to prevent data loss and faster performance.

-If you are using windows this option (i.e. safety removal and ejecting) can be adjusted from policy option (i.e. quick removal and better performance).

Short answer YES as:

Quite obvious if you tried to remove without safety option a clear message appears says 

"error" a file is being used in the background."

Or for better recognition next time you plug your USB flash to save time.

It keeps the cache enabled on non-removable drives, though—and sometimes it recognizes external USB drives as not removable, which is why your USB drivedoesn't have an eject button.

For the most part, yes.

even though most new USB drives (especially high grade ones) support the "Quick Removal" policy in Windows OS, which allows you to remove the drive without the need to safely eject, you will notice the performance of the file transfer/cache is pretty low, and it is more noticeable for USB 3.0

so, to get the most performance from your USB drive, make sure to set it for "better performance", and ALWAYS safe remove. 

Yes you need to because if you dont the usb drive might develop fault and moreso all data might be lost in the processs