For competitions, the performance benefit is zero time lag between controller inputs and the screen output.
Also, it's very very difficult to get the "look" right on an hdtv. The original graphics were intended to be displayed on a slightly "fuzzy" CRT, and if you care about the aesthetic, just transferring those same graphics to an hd-tv display often doesn't look right in a bunch of different ways. (Pixel aspect ratio, aliasing, frame blending effects, color bloom effects, interlacing artifacts, etc.) It's a very deep rabbit hole you can go down.
Also, it's very very difficult to get the "look" right on an hdtv. The original graphics were intended to be displayed on a slightly "fuzzy" CRT, and if you care about the aesthetic, just transferring those same graphics to an hd-tv display often doesn't look right in a bunch of different ways. (Pixel aspect ratio, aliasing, frame blending effects, color bloom effects, interlacing artifacts, etc.) It's a very deep rabbit hole you can go down.