How to safely and conventiently have an external drive connected to an OS X laptop
Actually, the assumption behind your question is incorrect. 

While other operating systems may manage the ejection of external drives differently (to some degree), they still require users to eject or safely remove them prior to physically unplugging them while the computer is still powered up.

The reason why this is important is that any computer (regardless of OS) can initiate a read or write sequence while it's powered up. It's important to note that not all read/write sequences are initiated by the user. Often they're initiated by the OS or other software, so even though you may think it's safe to remove that drive, it in fact may not be.

In terms of how you may be able to have this drive consistently connected so that backups happen automatically without the worry of damaging your drive, there's no 100% safe way without either ejecting the drive or fully shutting down a computer first. However, your next best bet is to ensure you close the lid of your MacBook prior to unplugging the laptop and taking it somewhere. By doing this and waiting a few moments the MacBook will go to sleep and unplugging the external drive will be safer (although not 100% safe).