To each their own of course...I go with the no ADRs system personally. I've in fact never made one. And I go to Disney every 2-3 months for 4-5 days at a time, almost always eat at table-service restaurants, and have eaten at just about every restaurant in Disney World. I go off-season, high-season, holiday weekends, etc and always manage a good meal.
Last month, I ate at Jiko (AK Lodge), Maya Grill (CSR), San Angel (Epcot), Le Cellier (Epcot), and Rainforest Cafe (Marketplace) over the 5 nights I was there. No advanced reservations - I called on the morning of that day to check for a table at Le Cellier and San Angel and made reservations for that evening for each.
I spent no time walking around hunting for a place to eat, never had to resort to counter service, and didn't spend any time with concierges tryign to find a place. I pretty much walked up, waited 15-30 minutes, then was sat down for a lovely meal.
There are strategies that help if you decide to try the no-reservation relaxed and free-style vacation:
1. Resort hotels are usually less fully booked and are a great idea for last minute dinner plans where you still want a high quality meal. They range from family style to 5-star, and getting in is easier than the theme park restaurants.
2. Eat at different hours. If you absolutely must eat at 6:30pm - 8pm, you're going to have a harder time, because that's when most families want or need to eat as well. Flexibility in your schedule or timing will make things much easier. Eat after 8pm, or during parades or shows (if you've already seen them, you're not missing anything), and you can get into pretty much any restaurant in the parks even on a holiday weekend.
3. Be flexible as to where to eat on any given night. I can eat at every restaurant I want to eat at, but not necessarily in a planned order. I might determine that I definitely want to eat at Tutto in Epcot, and call for availability - and maybe discover that tonight is booked, but there's availability tomorrow night at 8:30pm. So I'll book that, and then pick a different place to eat tonight. Maybe I had Jiko on my mind this trip - I'll go there tonight, and Tutto tomorrow...everything works out just fine!
4. Be willing to experiment. For whatever reasons, most visitors to Disney tend to stick close to foods they are familiar with - especially American tourists. So steak/American restaurants are much busier than the more ethnic fare. Le Cellier is practically bursting at the seams with reservations...Tutto Italia stays busy since Italian fare is well known in America. Even Boma is popular despite the African name because of the familiar meat dishes. Chef Mickey's, Cinderella's, Tony's, Liberty Tree, Coral Reef - the list goes on. And hey...I love those too, so no criticisms. But, I also enjoy trying all the restaurants out and trying different foods and styles when possible. And very good restaurants like Restaurant Marrakesh, Maya Grill, Nine Dragons, Teppanyaki, and the excellent Jiko tend to have pretty good availability even during the most crowded seasons.
Some people just can't relax or have fun unless they've got their whole trip pre-planned. Some people just can't relax or have fun if they know they have to stick to a schedule. Don't worry - Disney can accomodate both kinds of folks, and provide them a wonderful and memorable vacation!
On our most recent trip, when our DS(16) asked, "What are we doing next?", it was so nice to say, "Whatever you want to." 
More than once, he said, "This is my kind of vacation." We always have a set itinerary, but we didn't have anything planned on our last trip. Everyone actually enjoyed it more, which honestly surprised me. Now when anyone asked, "Do I need ADRs?", I'll be offering them possible alternatives rather than saying, "You must make them!". I do think it's possible, if you don't have DDP & don't care where you end up that evening.
...in two weeks it'll be tables for 1 
...Dec will be tables for two again 
