As others have said, the only time the lot at MK fills to capacity is Christmas Day itself. The rest of the year, none of the parking lots fill to capacity. We never stay on property, so we always drive. I agree with you that I like having the van and would not at all want to rely on Disney buses. Yeah, at MK you've got to take the ferry or monorail, but that's part of the journey for us, we look forward to it. From our experience, they fill up the lot one side at a time. For example, at MK, they seem to start with the hero's side, then move to the villains later. As others said, you don't get to pick where you park, the CMs direct you. It's luck of the draw. Sometimes you're at a spot right near where the tram loading is. Sometimes, you're aaaallllllll they way down the end of the row and it's a long walk to the tram stop. Just part of the deal. It's the worst at Epcot, the rows are super long. Then again, a trade off at Epcot is that for the first entire section of the parking lot, we find it quicker to just walk to the entrance than take the tram. Same for HS and AK. MK we almost always use the tram because you have to walk pretty far to get to the TTC in most cases (with some limited exception).
It's not really that big of a deal. We LOVE having our car available to us.