Yea, I've love to have a Cintiq but they are just a bit expensive =]
There are at least two issues to get beyond when drawing with a tablet
1. The awkwardness of drawing to the tablet surface while looking at the screen. Here all I can suggest is practice and line control exorcises. This is the learning curve. Practice inking comics - a skill where line control is essential.
2. The frictionless plastic on plastic feel. This can really screw up your line control. See below for a work around.
With the combination of those 2 factors I can understand why it feels awkward or just plain wrong. One trick I and many before me have found is to attach a peice of drawing paper to the tablet. The added friction/grip may be enough to give you the tactile experience you are looking for. Note however, the paper will begin to stretch/warp/degrade so you'll have to replace it every so often. You will also wear out your plastic nibs (pen points) much quicker but they are pretty cheap.
Certainly you loose something when switching to a tablet/digital solution but there are also benefits when compared to the traditional mediums. How digital tools find their place in your work flow is up to the individual., one is not necessarily a replacement for the other. I mentioned tablets because they are a viable alternative, at the very least an additional tool in your arsenal. As for animation... If you aren't comfortable with a tablet for sketching or precision work then obviously it will present problems.