1. When you change your own oil you can let it drip an extra few minutes and get a little extra sludgy old oil out.
2. As Larry says you can look for potential problems while under the car.
3. It's cheaper.
4. You need on hand a filter wrench and some filters and a case of oil. A jack and jack stands. With this modest equipment an oil change is not difficult. After you've done it twice, you can knock out an oil change with less hassle than is involved in leaving your car somewhere and picking it up.
5. You will do a much better job than many service centers because it's your car and you care about it. Certainly you will do a better job than any quick change place.
6. If something happened to the paint job you would probably notice right away. When you're looking at the motor regularly you gain that same sense of what the car is supposed to look like mechanically. So you have a chance to spot bad belts, fluid leaks, loose parts etc. early.
7. This is just an opinion here but I don't think it's practical to have a machine and depend on it and do absolutely no basic maintainance on it. It's asking for trouble.