Downsampling is really the basis of all anti-aliasing. The original anti-aliasing method, supersampling, was basically just rendering things at a higher resolution and scaling them down to your monitor resolution. And yeah, as you said it's way too resource intensive. Then from supersampling they went to multisampling, which uses some aspects of supersampling but in a way that has much better performance, but it also doesn't look as sharp. Now they have things like FXAA which are shader based, it has very little impact on performance but also doesn't look great, it basically just blurs the edges instead of actually anti-aliasing them.
Running SSAA, MSAA, SMAA, TXAA, FXAA or any other anti-aliasing you want and downsampling will look much better for screenshots than just increasing the resolution larger than your monitor. It's like having anti-aliasing ontop of anti-aliasing. Even having a bunch of anti-aliasing on and scaling 3200x1800 down to 1080p, the screenshots of the game look better than the game did running in real time. I'm guessing this is partly due to Photoshop's bicubic resampling, I think it does a better job of keeping the sharpness of the higher resolution than the scaling on my monitor.