I think you have that arse about face. Games are tailored to the capabilities of what the hardware can do. The NES' gimmick was fast hardware scrolling and sprites. Platform games benefit from that, but you can hardly claim Zelda 1 was a platform game, nor things like Punchout. The SNES's gimmick was better graphics and sound and the famous mode 7 scaling and rotation. They looked for games they could develop to show that off, and that's why F-Zero was a launch title, and Mario Kart began life as a multiplayer version of F-Zero.
New consoles are released when there's something worthwhile about them that the company feels will make you buy a new one. Be it better graphics, better controls, bigger games, or simply an anticipated game they've held back to only release on a newer system. If they can eeek those improvements out over more systems, they will so they can sell you more things.