Will "backup -> factory reset -> restore" free up space?
Your suggested backup/restore process will only provide a temporary respite. Caches will be cleared, but they will regenerate. 

In iOS 11 Settings > General > iPhone Storage will give you recommendations as to how you can free up some space. 

You can offload apps (delete the app but leave it's data, settings and icon) and you can store your photos in iCloud. 

You can process your photos using something like JPEGmini or Half.app and regain some space. 

But really you're fighting a losing battle. I recommend you upgrade to a larger capacity iPhone so you don't have to waste time and energy on keeping things just below capacity.