Why did the Atari's have such clear displays?
I suspect it might have something to do with all the shielding
No. As usual it's about the effort the designers did put into the display. To reduce cost, the VIC-II outputs an already internally mixed B&W signal and chroma. While this is basically like S-Video, the quality is defined by the internal generator - and doing analogue on a primary digital process is always a challenging task - especially if one want's to save money like Commodore did. In addition the external circuit is rather frugal.
In contrast the Atari's CTIA/GTIA output is fully digital and gets further 'sharpened' by a 4050 CMOS inverting buffer. Thus these signals are already way more 'clean' before geting mixed in a somewhat more elaborate diskrete analogue section. Here is a nice page showing the circuitry in detail for the purpose of an easy modification to get an S-Video compatible output.
Also the modulator used, at least for the 800 is of a better quality than the one for the C64 - but that's only relevant for TV, which is less than desirable anyway - still, here the Atari outperforms the Commodore as well.
I guess it pays out that Atari designers had quite some experience with TV/colour when creating the 400/800 output circuit.