There's a Drop Off area for MK. It's the parking lot that is next to the Lost and Found building. It's situated between Lost and Found and the Poly.
For Epcot, you could always drop someone off at BWI or Beach Club and they could enter through International Gateway.
This s true, but you kind of have to know how to get there- so to speak. In a way, all roads lead to the MK parking lot. Beyond that, I'm not sure it would be worth driving to one of the resorts, then having one person go back and park. You also go to the car when you leave the park, and you'd park that much further away.
As others have said, there are pros and cons to each. Driving means you must have a designated driver! Cars get hot; buses have AC. (then again AC when you are wet may be too cool!) Boats and monorails are fun! It is not always clear how to get from point A at WDW to point B at WDW, and especially getting offsite (Do use your GPS!). hen again, sometimes monorail stop running mid-day. Many buses make multiple stops. Your car has a trunk and seats for everyone. (don't underestimate how unpleasant it can be to sit aside a sweaty stranger!)
You probably DO want a picture as you are entering WDW property.
Last, the wisdom of always driving- and getting to MK - depends a bit on which resort. If you are staying at an Epcot deluxe walking to Epcot/HS is probably a better bet than driving (there's also a boat). you'll enter Epcot via the IG. If you are at CR, then walk to MK. If you are at another monorail resort- then use that for MK.
Also, it may be better to drive to MK - if you are also going places other than MK. Like if you plan to go to MK then directly to dinner at AKL, then back to your resort at 9pm- you should drive for the day. Getting to resort via WDW transport can be time consuming. Conversely, you can't park just anywhere. Parking all day at a resorts to go to a park is a big no-no.
Foul weather can add a toss up factor.