In fact, there are a number of 2d games that do use what amounts to vector art; Capcom's Ghost Trick:Phantom Detective, for instance, essentially generates its in-engine characters as vector graphics. (To be more precise, I believe they're given as flat-filled polygonal regions, which in this case amounts to the same thing). More broadly, polygonal models in general can be thought of as 'vector' data - they represent the vertices, edges and faces of an object - as opposed to (screen-resolution) 'raster' data, so in some ways most 3d games are using vectorized data descriptions.
But I suspect your question is more about 2d art, and there several factors come into play. As Mr. Beast says, small details make vector art quite a bit trickier to construct; imagine something like a grenade belt on a character, where even a bit of clever copy-paste of individual grenades still isn't going to save a whole ton of time on the effort. I think the bigger issue, though, is that vector graphics take some control away from the artist; as you note, vector art may look substantially better scaling up, but the real issues are at lower resolutions, where the fiddly details of rasterization can substantially change how an image looks. Imagine a character's eye, for instance; the outer boundary might be an oval no more than ten or twenty pixels across and possibly just a small handful of pixels in height. At those resolutions, how the vector data - be it lines, circular arcs or Bezier curves - is rasterized becomes a critical issue, and unless your artists can work directly in-engine - which essentially means creating an entirely new vector drawing program - then they have a hard time guaranteeing that the appearance of their objects in-game will match the appearance in their tool. What's more, just appearing correct at one resolution is no guarantee whatsoever that they'll appear correct at any other; again, the scaling works well when you're dealing with objects where the details are dozens or hundreds of pixels in size, but as you get down towards smaller-scale features then your scaled rendering runs into exactly the same rasterization details.
That said, vectorized rendering isn't always inappropriate, and it can often be a stylistic choice to excellent effect. But it's not a panacea for the issues you raise with raster graphics, and it raises new issues of its own too.