Correct, vectors cannot be displayed on a screen, because a screen is an array of pixels, so everything must be rasterized. 3D models themselves are in fact vectors (usually straight lines, but curved surfaces are possible by rendering to lines first). And then the GPU does the work to translate this into pixels. That is basically the only thing the GPU does, is convert vectors to pixels and then warp images onto them. There are ways to accelerate this on the GPU, for example for font rendering, but it is niche and not built into the hardware.
Vector illustration also must be converted to pixels before doing anything with it. Even Flash, which I used quite heavily in the 2000's could not display vectors, only pixels. They had a run-time engine that would do this on the fly on CPU, but it was quite slow and also the main reason performance sucked on Flash games. Later on you could pre-render to bitmaps and this increased performance about 100 times or more. There is really no good reason to ever use vectors at run-time as they cannot be displayed in any case, you are just offloading a process that should be precomputed to run time on a users computer, with no visual difference (or even a loss in quality, most likely, because precomputed rasterization can use higher quality algorithms than run time, especially if your users are on old computers). So it's pointless.
That said, there did used to be actual vector displays. Like they used on the old Atari game Asteroids. In that case they used a CRT-era display, but instead on having the ray gun move in scan lines, they moved it arbitrarily to draw vector lines on the screen. It was amazing, and basically infinite resolution and infinite refresh rate (or at the very least beyond the human eye). In theory, we have the technology today to make a true full color vector display using a micro-mirror array (similar to how DLP projectors work) but I guess there is no commercial interest since it would have very limited content and 4K pixel based video already looks basically real.