This is a good explanation. The only time the Subwoofer setting offers "LFE only" is when the fronts are set to "Large" - which is pretty rarely going to be the ideal setting.
If you have fronts that should be set to "Large", you still will typically have center and surround speakers that should be set to "Small". Those speakers will then use their specified crossover points to redirect low frequencies elsewhere. If you have the sub set to "LFE only", the low frequencies from these speakers will go to the front speakers. The "L/R+Sub" setting will share some bass between the fronts and the sub. The "No" setting will disable the sub entirely, and the fronts will get the LFE channel and any redirected bass from other speakers.
This bass management matrix can be a handy way to see the logic for different situations.
If you have the fronts set to "Small" (which is how I set them even when I had Paradigm towers that went pretty low), this all changes. The sub only has one possible setting once the fronts are set to "Small" - "Yes".