Live USB booting has several benefits, including but not limited to:
OS Portability and Convenience: Flash drives are small and easy to carry around in your pocket, which makes them convenient to use for booting from USB operating systems or system tools — while on the go. For example, you might use one to temporarily USB boot from a Linux, allowing you to run your own portable OS on a computer at a friend's house, while at school, from your work PC, or when traveling.
USB Boot from Multiple Operating Systems: A variety of operating systems including Windows, Linux, and FreeBSD can be booted from a flash drive. Making this a versatile option for troubleshooting, running specialized software, testing out new operating systems, and installing them.
Boot from USB for Privacy and Security: Can be more secure than booting from the computer's local hard drive because it isolates the operating system and any files on the removable drive from the computer's internal storage. This can be useful if you are working from a computer that you don't trust or if you are worried that you might encounter malware or other security threats.
Operating System Recovery from USB: If your computer's operating system is corrupted or you're experiencing other issues, you can boot from USB into a recovery environment to perform a fix or install a fresh copy of the operating system.
Fast Solid State Speed: In some cases, a removable drive can be faster than booting from the computer's internal hard drive, especially if you're using a super fast SSD flash drive and the internal hard drive you are working with is old or slow.
Cool Factor of USB Booting: The ability to bring your own custom Live portable operating system with you to plug in and run from any computer brings about envy because it's just so satisfying and cool. Once others see what you can boot from USB flash media, they want to do it too!
As you can see, USB booting can be a convenient, versatile, fun, and secure option for a variety of useful tasks.