As a energy conservation rule, if you are not using the machine, it should be powered down in some fashion: shutdown, hibernate or at least standby/suspend.
If you are going to trigger the machine into use, it could be configured to 'wakeup' on the trigger.
If you like to keep your browser open on multiple tabs,
these days firefox allows you to remember your sessions right up to the scrolled location on a page -- so, save-and-quit to restart.
Another reason to choose no-shutdown or partial-shutdown is a quicker restart.
This is when you don't like waiting for the machine to get back in action.
You could optimize your machine for a better response to work-around this limitation.
Having said all this, the other question is -- is there harm in leaving your computer up all the time?
Not over the typical lifetime of a machine.
Servers are up all time and many desk machines are up all time too.
There are usually hardware and operating system defaults that will make parts of the system slow-down or sleep when not in use to help here.