I used DME twice, loved it twice.
Smart travelers flying ANYWHERE pack a carry-on with items they'll need for the first 12-24 hours just in case the AIRLINE delays their checked luggage. If you do this, then having your luggage follow you by 3 hours or so really shouldn't make any difference at all. If I was flying to, say, Phoenix, landing at 2:00 p.m. with 7:00 p.m. dinner reservations, I wouldn't be caught dead with my nice dinner clothes in my checked luggage. What if my suitcase gets delayed by the airline???!!! Then I can't go to those nice dinner reservations I made months in advance! So I pack what I need in my carry-on, then I have nothing (immediate) to worry about.
With DME, the checked luggage gets delivered to the inside of your resort room whether you're in there or not (Bell Services/Luggage Assistance CMs are pre-tipped by Disney for the luggage delivery, so it's not like they lose out in the affair). In other words,
there's no need to wait around in your room for your luggage to arrive.
The first time I used DME was on its 4th day of operations, back in May 2005. We checked in around 11:00 a.m. or so at CBR. We went to the food court and had lunch and walked around the resort, then went back to our room to change into pool attire (which was in our carry-ons), then went to the pool. When we got back from the pool, maybe around 2:30 p.m., our luggage was in our room waiting for us.
The second time I used DME was about 8 weeks ago. We checked into POFQ around 11:00 p.m. I had planned to ask that our luggage be held 'til morning, but I forgot to request this. Around 1:15 a.m., we got a phone call saying they had our luggage and asking if we wanted it now or in the morning. Um, morning, please

... zzzz .... I called for it around 6:30 a.m. or so and it came a few minutes later.
My experiences are pretty typical. Are there some negative experiences out there? Sure. No system is perfect. But also realize that DME has served roughly 3.5 million guests so far, and there are VERY few reported problems. Of course, when you have a problem, you tend to let people know, and when everything went normally you usually don't say anything unless asked. What I mean is, you almost never see threads with titles like, "DME delivered my luggage as planned," or "Mousekeeping cleaned my room every day and left me towels."
DME has worked very very well overall. It was very convenient, and best of all, FREE.