You would much rather have it go down the mounting pole or your ground rod than down your wiring. Without proper grounding, lightning can do some really strange things, and can jump around all over while trying to get to earth. If your inverter happens to be in the way, you will probably be buying a new one. You cannot stop lightning, but you can often direct where you want it to go. That is not their purpose.
Lighting usually lasts for only a few microseconds - much faster than any fuse or breaker can blow.
It's pretty unlikely that a one-inch fuse gap is going to offer much protection from a bolt that just cut through two miles of open air. Yet the myth persists that a fuse will offer lighting protection. It will not. The importance of a single-point protection ground cannot be stressed enough. All equipment should be bonded to one single earth ground.