"Story in a game is like a story in a porn movie. It's expected to be there, but it's not that important." - John D. Carmack
Despite coming from one of the big names in the games industry, I despise the above quote and the attitude that it represents. It denigrates games as an inferior artform, or even as something that is not an artform at all. Game designers are expected to merely entertain people, not to reach out and affect them in that deep and subtle manner that high quality art does.
Games are their own unique artform (or artforms really), so they have their own unique challenges and opportunites when it comes to telling a powerful story, but the fact that there are challenges is not an excuse not to try to meet them.
When I tell people that I play games for their stories, I often get strange looks. And it is true that I do play and enjoy games that treat their stories in a kind of tacked-on way. Plants Vs Zombies comes to mind. But when I stop and think about why games matter to me, and why I am willing to dedicate so much time and effort into developing games, those aren't the experiences that I tend to remember.
I remember the majestic colossi of Shadow of the Colosus, pulling the legs off the spider in Limbo, and Shodan's reveal in System Shock 2. It's not that I could not have found these stories in some other medium, but the way that these games drew me in and placed me in the role of the protagonist gave the experience something that other mediums cannot. In Limbo I fealt fear when I grabbed those spider legs and disgust when they pulled free. In Shadow of the Colossus I felt unease and guilt as I prepared to kill something grand and majestic. Things I couldn't have experienced if I were merely watching from the outside.
Would Plants Vs Zombies have been a better game if it had had a deeper story? I'm probably going to be contraversial by saying this, but yes.
To be sure, not just any story would do. Plants Vs Zombies is a silly, funny game. It would have needed a silly, funny story. A comedy in fact. Maybe someting about a gardening competition that due to the stubborness of it's competitors keeps on going despite being interrupted by a zombie apocalypse.
I realize that crafting a good story for your game can be a big thing to ask. To develop a game your team already has to create the code, develop the art, and ensure that the gameplay is fun, and now I want you to tell a good story too? You probably aren't experienced in crafting a compelling story either, since while there are schools that will teach programming, art and even game design, I know of none that teach storytelling in the context of games. And if you do have some experience in telling stories, you probably learned it in another medium and so have just as many things to unlearn as you do new things to learn.
I know it's hard, but if you weren't willing to try and do hard things you probably wouldn't be trying to make a video game in the first place.