We've visited with and without parkhoppers, but here are the three things we appreciate most when we have them:
1 - Avoid lines: we can make use of morning EMH at one park, go back to the hotel for a midday nap, and then go to evening EMH at another park (or simply hop to a less-crowded park of our choice if we don't like the line lengths where we are).
2 - Tour efficiently: the fact is, HS is a less-than-1/2-day park for my family. AK is a 2/3-day park. Epcot is a 1.5-day park and MK is a 2.5-day park. With park-hopping, we avoid having to pay for full-day tickets for all of those partial days. We can park-hop for 5 days instead of having to buy single-day tickets and hotel accommodations for 7 days. (That being said, there are people for whom each park is a full-day park. It all depends on what they want to do and what pace they prefer to adopt.)
3 - Be spontaneous! Anytime we find an unexpected pocket of time, stumble on an attractive ADR somewhere else on property, have friends/family in the parks that we'd like to join for a meal or a park visit, or want to return to a favorite attraction "one last time," we can just do it, without fear of "wasting" a full-day ticket.
Granted, we only tend to find parkhoppers "worth it" if we know we're likely to use them to hop at least three times, and/or if they're going to get us an added benefit (e.g., upgrading to hoppers to be eligible for a discount or promotion that will save us more than the cost of the hopper upgrade itself, or upgrading to Parkhopper Plus if we're going to make use of at least two of the more expensive "entitlements").
Overall, I do think the benefits of hopping are, as the title indicates, "misunderstood..." but perhaps only by the thread's author!