Yes, thats true. AA was helpful at certain resolutions that were what I call "medium resolutions", the range between 480 and 768 pixels. But CRTs still had a softer image simply as a byproduct of the way the technology worked, and worked better at lower resolutions like 240p (AFAIK, any signal less than 480 vertical pixel resolution was automatically progressive scan). This was abused and exploited by game developers of the time, famously utilizing dithering for transparency effects for platforms that didn't fully support it such as the SEGA Saturn (it only supported transparent 2D sprites, but not textured polygons like the PSX did). The softer image led to the dithered effects smoothing out, giving the appearance of a bigger available color palette and special effects. Flickering sprites every other field was also a common technique due to CRTs high image persistence. This is why games like Streets of Rage look awful on modern displays, but display correctly on CRTs.

But regardless, AA will probably be phased out eventually, its just a tool to mitigate growing pains of new display technology.

I'm not that guy, but I don't think so. The trend will likely be that we get to the point where we render and display in such a high resolution that you can't even see pixels anymore. We're getting there already with smaller 4k displays where turning on AA doesn't have an appreciable difference in 4k native rendering.