I have struggled with this issue as well and my son will be 4 in two weeks. I tried to encourage, praise, help, work together, give choices, all of the "soft" techniques, to no avail. I would try for a week or so and then give it up for a couple of months until he was ready. Now that I have a second on the way I realized that it is really important to me that my son is capable of getting himself dressed, at least some of the time, so I made a more concerted effort - just this week!
Here is what I did:
FIRST - I allowed an extra tweny minutes or so to our morning time so that I knew we had time for my child to succeed (you will see what I'm talking about below).
1) First of all, no play in the morning and no breakfast until we are all dressed, to the shoes. We had some pretty bad habits of responding to requests to "play with me" before we were ready and we were always rushing out the door. Or we would spend sooo much time working with our son to get dressed that we were eating in pj's. We now tell him "work first, play second" and it is simple and logical and he gets it. I wish I had been taught more of this! The first few mornings were very difficult. A lot of crying and resistance. One thing that helped was laying his clothes out in the hallway so there were no toys for distraction.
2) IF he gets ready fast enough that we are done with breakfast, potty, toothbrushing, and face washing and still have time before leaving, he gets 10 uninterrupted minutes of playtime with a parent. This takes discipline on the parents' part to be ready to go, but it is worth so much to a child, especially prior to a day of separation. He LOVES it when the phone rings and I say "oh, I can't get that right now because this is our playtime."
3) IF there is still time left after 10 minutes of play, he can watch a video while the parents are finishing up and then we leave. This is usually only another ten minutes so I don't feel weird about it (I'm pretty limited with tv watching).
4) The last thing was a sticker before leaving. I expect this part will only last another week.
And of course, LOTS of praise and appreciation.
RESULTS: Days 1,2 and 3 were pretty hard! Lots of tears, some cajoling, helping, bargaining, etc. But then I learned to walk away, busy myself getting ready and check in only every 3 minutes or so, and that really helped. Days 4 and 5 were really quite easy! He has gotten the playtime, video and sticker every day. By day 5, for the first time EVER, he did all the work. (socks are still tricky so I try to give him really easy ones)
PS I do believe that some kids are just less driven to be independent, at least at different stages. My son never, ever said "me do it!" He is a "spirited", "strong-willed" child who persists in requests for help.