Why is attack damage, movespeed, etc. visible on enemy champions, but not crit chance, cdr, etc.?

I'm guessing for clarity and neatness. If you display every stat on a given unit things can get complicated pretty fast. Rather than sand under a microscope you just get sand.

http://sandgrains.com/MauiPieces-2-web-copy.jpg

If you add to much information it can easily reach a point where it defeats the purpose of displaying that information. It doesn't look neat or helpful, but just offers and overwhelming display of stuff. The most relevant thing here concerning clutter isn't so much the actual display, but the HUD being taken up by a big display. When a lot of champions can easily have 0 crit or 0 CDR for an entire game, you're taking up screen space that could be better served showing something else.

Also - you can always bring up the display screen showing the levels of every hero and their items. For me it's bound to O, think TAB brings it up to. CDR and Crit items are usually pretty easy to find in that, so if you know what items do you've generally got a solid idea of how an opponent or ally is going to act and if they're investing in things like crit, CDR, tenacity, healing effects, %auto-attack reduction, etc. You can also just click on opponents and see there items.

Its kinda weird but it is visible.

Most champions have a crit animation. The only reason it is pointless to see when the enemy will crit you is because once the auto is let loose, it will travel towards you anyway.