Thanks for the input!
I think it really depends on what kind of game you are designing. Personally I love games that tell rich stories. So this is also the type of game that I am interested in building! The challenge for me (and for all games with an emphasis on story) is how to design mechanics to reinforce certain ideas/themes etc. Recent example being in Wolfeinstein II. You play a sequence of that game @ 50 health instead of 100. It's a small thing, but it reinforces this narrative point that BJ (the player character) was severely injured and not fully healed yet.
On the flip side you can also have very mechanics driven games such as Super Mario Brothers wherein the story falls second to how the levels are designed, how the responsive the controls are, etc. These challenges can be difficult in their own way! Part of the reason why I love games is that there is such diversity in the genre of games.