There could be other causes but as James notes in the comments, a big mistake is putting the paint on too thick. The first coat should be somewhat transparent. And it's not necessary to thin the paint, it's how much you put on the roller for a given area. The other thing is that you might want to buy a better-quality paint. The cost difference between paints is largely due to the amount of pigment. A cheaper paint typically means you will need more of it to get the same amount of pigment on the wall.
As you note, this approach will leave a poor looking end patchy result on the first coat. But that's actually what you want to achieve the best results. A very thin (patchy even) coat. By the time you come around a medium sized room, it should be ready for edging. Go around all the edging and it should be ready for a second roller coat. With big-box-store paints, I'll do 3 coats at least. With a higher-quality paint, I can often get away with 2. This sounds like it will take a lot longer but because you are not trying to get a perfect opaque coat, they go up fast. You also don't need to wait days between coats. As you add coats, the patchiness should disappear. Once I'm done with that, I'll go around and touch up any patches that need a little more coverage.
The problem with thick coats of paint comes down to water. For the paint to dry, the water needs to come out of it. There are two places it can go: into the wall surface or into the air. The wall surface will only absorb a small amount, so the rest needs to go into the air. With a thick coat of paint, a skin will form before the water from the rest of the paint layer can migrate to the surface and evaporate. This will greatly slow the drying and if you put another coat on before it dries, you make the situation even worse. Extremely thin layers avoid this entirely.
When using tape (I don't typically bother with it and free-hand edges with a good brush and a wet rag/paper towel at the ready) you can get better results by taking a small brush and lightly painting over the tape and its edge. Let it dry and then do your main painting. This will give it a cleaner 'break' and also help keep paint from getting under it.