It's useful for quick debugging on websites. I'm not a web designer, so when I designed my site it was useful to consult with people I knew were good at it. They could check out my site, view the source I'd put in and test a potential change using the tools available in Firefox.
Of course, those changes wouldn't stick because then they'd effectively be saving the version of the website stored on my web server.
By your logic, anyone should be able to inspect and subsequently alter the source of any website, with their changes being saved to the web server. This would effectively give anyone free reign over editing websites. Can you imagine how chaotic that would be?
i didnt say it was the only way. there can be more than one way to do something. when i was working on my firefox plugin (which failed because i cant get javascript. damn you ultra weakly typed oop!) i would inspect elements so i would know what i would have to target