I'm not sure this is a consequence of the phosphors. It looks to me like this is an effect of how quickly the electron gun turns on and off. I would expect the horizontal sweep rate to be unaffected by whether pixels are supposed to be on or off, so the blurring at the left edge is determined by how quickly the beam ramps up to full current when turned on, and the blurring at the right edge is determined by how quickly the beam current is switched off.

The slow decay of the phosphors is on an entirely different timescale: more on the order of the time taken to refresh the entire screen, rather than the time taken for the e-beam to sweep across a single pixel. The asymmetry in the phosphor's activation vs decay is vastly greater than the asymmetry in the electron gun's switching on and off.