Agreed. Note that the OP asked about regular maintenance. For special things or oddball issues I'd likely go to the dealer. But routine things like fluid changes, brakes, filters, etc. I think the dealer expertise is not worth what you're going to pay for it.
Actually, it's not that uncommon that the dealer service techs have less expertise than a good independent. And my local Mazda dealership has proven this to me which us one reason I do my own regular maintenance. I had a Ford dealership over-fill my 2010 F-150 by over a quart of oil. This happened 25 minutes after I told the service writer to tell the service tech that my truck had the 4.6L V8 and took one less quart than the more popular 5.4L engine. The service writer looked at me and said something like "yeah, yeah, they know how much oil the different engines take". I said, "No, really, just mention it to him because I'm in the middle of a cross country trip and I don't want to deal with something like that." He said, "yeah, ok, whatever." On the drive to my hotel room I thought the engine sounded kind of "gurgly" or something. When I arrived at my hotel I checked the oil and, without even giving it time to drain, it was way, way past the top mark. But the dealership was closed for the day. The following morning I took an extra 2 hours out of my day to return to the Ford dealership and show them what they had done. Yeah, they were pretty embarrassed. Two lessons here:
1) Yes, even dealerships screw up (even when you warn them of the specific thing you do not want them to screw up).
2) Even routine maintenance is difficult for some serve techs, dealership or not.
That's why I qualified my original answer. It totally depends upon the quality of the dealership/independents in your area. BTW, not all dealerships are more expensive than all independents. The oil change at the above Ford dealership w/ 5 quarts semi-synthetic and filter was only $29.99.