USB drives, can only be written to a limited number of times, normally thousands, and then they don't work.
The life of a USB drive, can be maximized, by minimizing the amount of writing to it.
Reading the drive, does not shorten it's life, only writing to it.
Some computers contain solid state internal drives, similar to usb drives. The same thing applies to these drives.
There are a number of things which can be done to maximize the life of these drives.
Never put a swap partition on a USB drive, as this results in a lot of writing to it, and will greatly shorten its life.
Use a non-journalling filesystem to minimize the amount of writing to the drive. When installing Tinycore, ext2 is ideal.
If persistent opt is used on a USB drive, in most situations this results in less writing to the usb drive. Most people change settings in opt, less often than they backup.
Is it a good idea to have persistent home on a USB drive?
It depends on how you use the USB drive. For example:
If you run Tinycore from a USB drive, and normally change a lot of files when using it, it may be better to backup the home directory.
If you use the USB drive as a repair and rescue tool, and don't normally change many files when using it, it may be better to use persistent home.
Ask the question: Is less written to the USB drive by saving files each time they are changed, or by saving everything in backup each time the computer is turned off?