So its a balance between error correction and error introduction. In Bacteria its worth it, in humans not so much, especially as we have a bunch of other subtler more complex ways of handling viruses before they get all the way to the nucleus https://en.wikipedia.org/wiki/RNA_interference Bacteria dont have this luxury as their DNA lacks this extra barrier. The biggest difference is simply cells dont matter in a human and can just kill themselves if all else fails.
The rest of the "innate" immune system has similar proteins involved nearly everywhere e.g. https://en.wikipedia.org/wiki/Toll-like_receptor These are the components involved in cell surface recognition of sugars. But much more similar between all animals than animals and bacteria.
Answer to your second question is yes you could add a CRISPR construct with templates for known disease and add artificial immunity. However, finessing this so that CRISPR doesnt cause lots of damage from randomly cutting your DNA throught your life leading to a higher risk of systemic cancers... is a big hurdle.
The crux of the debate is that mammals have the interferon system to respond to viruses, so why would they have kept around a system like CRISPR?
Would it be possible to introduce a genetic template from a viral disease into an embryo to produce a human essentially immune to that virus?