OK, so the asset is sharp when it's 956×956, but you then put it in your comp and scale it down to 50% meaning that it is now 478×478. It looks softer than it did at full resolution. Yes, what did you expect to happen? It has lost 75% of the pixels it originally had, it's going to look softer, end of story. Export from AI at the same pixel size that it's going to be in the comp and that's the resolution you have to work to. If it looks too soft, then change your design.
Video is a raster format. If you put something in a comp it is going to be rasterised, and if you make it teeny tiny you may run out of pixels. That's what designing for the screen is all about. You've only got a grid as large as your final resolution to play with.
Let's put it into perspective that will help you visualise it from a print designer's view. If you were designing for print with a dpi of 300, your 720p video frame would measure around 11cm × 6cm (4.3" × 2.5"). Not very big eh? For something this size you wouldn't put in elements with tiny details and expect those details to look super crisp on the final result. Same for video.
Tiny details will get antialiased and look soft - when they're compressed you will lose even more detail. Your job as a designer is to design stuff that looks good at the final resolution. (And if you think that's a drag, try designing for standard definition interlaced content delivered on VHS tapes. You kids don't know how good you gots it).