Hi Steve, welcome to The Escapist. Let me welcome you by utterly disagreeing with you.
We're friendly that way!
Genre is a problem, of course, but it's also a tool. It's worth noting that the problems you're describing with genre exist in other media too. Sure, it sucks that every MMOG brings in looting, but how often have you heard or read of a fantasy dwarf with a Scottish accent? Exact same issue: Convention becomes so strong it's hard to escape it. This is far from a unique problem with games, it's a problem with genre.
But you know what? We keep using genre. Why? Because it's a great tool for a number of reasons. On a marketing level, it creates a built-in fanbase. On a creative level it provides a useful starting point and creates limits that allow the creator to consider the creative space his work will employ. On an artistic level... OK, there? Genre kind of sucks. But even there, good genre works will find ways to either deconstruct or subvert the genre.
As an example, Far Cry 2 is as solidly a shooter as you'll ever find; but it won considerable creative acclaim (as well as a lot of critical distaste) because of the way it subverted the shooter genre; missions were designed in counterpoint to your story rather than to support it, thus leading to a logical conclusion when, while suffering hideously from malaria, you destroy whole stockpiles of the very medication that could save you. The message that war is irrational, violence meaningless was supported. This is solidly supported with The Escapist's experiential leanings, but it's not a lesser game because it exists wholly within one genre.
For another example, consider the works of Fumito Ueda. Ico was, at its heart, nothing but a puzzle platformer. But y'know what? It took that genre and broke it down to its pure core. Nothing extraneous. No HUD. A solid logic for the basic 'find a path' gameplay logic. It found its emotional core in the AI that created the relationship between Ico and Yorda. And it was magnificent. Shadow of the Colossus, while engaging in a bit more genre-bending, was similar; it really was at its heart an action-adventure game not dissimilar from Zelda. Sure, it stripped Zelda down a lot, and mixed it up with a light-puzzle boss fight mechanic, but it's hardly suis generis. And it was the absolute standout favorite example for people trying to defend the idea of "gaming as art" to Roger Ebert -- for a reason.
As an opposing example, my favorite whipping boy, Farenheit. (I suspect Heavy Rain will kick in when I finally play it.) It's genuinely suis generis, with few games really like it in any way, shape, or form. And y'know what? It's a goddamn mess. Instead of using well understood, appropriate and familiar mechanics to, say, have the player escape a parking lot unscathed during an assassination attempt, it shoe-horned in a whole new set of mechanics that undermined the player's authority and distanced them from the action. It was awful.
Genre is a tool. It's no wonder games have been saddled with a pair of them since, like it or not, "interactivity is the one element that most separates gaming from other forms of media". An RTS is not an FPS, and neither is an RPG. You could do a war tale in each one of them, but it still wouldn't be the same game or story no matter how hard you try. That's not a bad thing, but it's a good solid argument for coming up with your story, then chosing a genre.