The really unfortunate part, and the reason I started getting irritated was it makes it seem like the Doctor can't learn.

it is what disappointed me most with EoT -- he never learns, he never finds peace, he just dies. it actually really upset me when i watched it. three had to die to learn not to fear death, and to throw off the last bits of his exile, but we see him accepting that before he does actually die. and ten doesn't. :(