But not in the way that they were meant to be played. Does that often cause issues with in game abilities?
It could. To be honest, the only game I've played on the DC that requires use of the analog stick is Beserk.
Required, maybe...
useful is a different story.
Take Gauntlet Legends for example. You can have a perfectly fun game using just the d-pad, but it is much much better with the analog stick. Running full speed all the time can screw you big time, like if you have to walk right up to a ledge/enemy/etc. If you are going full-on, you can overshoot it.
Virtual Tennis is the same way. Running full-on can make you overshoot the ball. Not enough to miss the ball all the time, but enough to where you can't have precision placement over where you hit the ball. (Someone on here a while back said VT didn't utilize the analog controls, but this is just not true.)
There are many more games with these same kinds of problems.