For me, Extra Magic Hours (EMH) was never an advantage to staying on-site at WDW (different story at DLR). In fact, at WDW, I typically try to avoid parks with EMH.
For me, the advantages to staying on-site are as follows:
1. Have 60 days instead of 30 days to book FPs (this can mean the difference between getting a FP and not getting one at new, popular attractions).
2. Have 180+10 days to make ADRs (this can mean the difference between getting an ADR and not getting one at very popular table service restaurants and/or getting and ADR at a popular restaurant at a decent time).
3. Transportation-related benefits. Specifically, don't have to spend time/effort doing the following: baggage claim, rental car counter, driving, parking, airport baggage check. In fact, one of the reasons we specifically like on-site WDW vacations is that they are almost the only kind of vacation that allows you to skip every one of these.
4. Complimentary magic bands. It's so nice to have one item that acts as a hotel room key, park ticket, fastpass ticket, and credit card that you don't have to dig into your pocket or wallet to retrieve. And you can even wear it in a pool or at a water park.
5. We just enjoy the atmosphere and theming of WDW resorts, at least at the moderate or deluxe level. Along those lines, we are not park commandos and spend at least half of our waking day at our resort (I would much rather be at a resort swimming pool between say 1 and 5 pm than inside a theme park).