SMAA and FXAA aren't very good with image stability, they are PS3/360 era solutions and belongs in the stone age. MSAA doesn't work with forward renderers which is 99.9% of games, where everything is rendered on top of physical geometry and thus can't be picked up by the edge detection & smoothing process.
TAA works because it's cheap, accumulates multiple data points over time (hence 'temporal') and provides best-in-class image stability, especially at higher resolutions. It can also be used for DLSS/FSR to piggy-back off of.
The obvious drawback is that it is extremely reliant on data, if the resolution isn't quite high and the framerate isn't quite high, it can look blurry especially in motion. You really need 1440p/60fps+ and above to get the best out of it. Most of its critics tend to be those running 720p-1080p displays at lower framerates, especially console games