It is not hard to calculate the bandwidth used by AF.
4x uses 32 textures samples
16x uses 128 textures samples
In a 1920x1080p scenario you have for each pixels the load of 32 textures samples in 4x or 128 texture samples in 16x.
That means:
4x: 8294400 textures samples loaded per frame
16x 265420800 textures samples loaded per frame
Normally you have 4 bytes of data per texel.
4x: 33,177,600 bytes per frame
16x: 1,061,683,200 bytes per frame
Or in a 60fps game:
4x: 1,990,656,000 bytes per second = ~2GB/s
16x: 63,700,992,000 bytes per frame = ~64GB/s
Of course these are raw bandwidth numbers.... texture compression and cache reduce it some time or other but the bandwidth needed for 16x AF is way bigger than 4x... plus I give you a 1080p scenario... 4k 60fps is another talk:
4x: 64GB/s
16x 255GB/s
That is the biggest issue on consoles because you don't have two pools of RAM.
The use of AF in PC doesn't harm the CPU bandwidth use... so you do AF while doing others things on CPU.
But on console the more the AF eats the bandwidth the more the CPU is harmed and can't do things due not having enough bandwidth.
In 4k 60fps the 16xAF, disconsidering the texture compression, will eat almost half of consoles bandwidth.
I truly understand whey they set the base on 4xAF... even in the worst case it will just take 64GB/s of the bandwidth in 4k 60fps games.
Edit - I forgot to point that PC CPU + GPU bandwidth is way higher than actual consoles unified bandwidth when you look at similar GPUs... plus low and mid-end GPU users usually set their games to low resolution and framerates that makes AF bandwidth use smaller... just these with big GPUs running 1440p/4k at 120/144fps will have a big use of bandwidth by AF but theses GPUs have enough bandwidth to do everything.