The closest thing we have had is URF which is I think is as close as you can get. This would cause huge problems.
No CDR Limit - the problem with this actually isn't about damage spells but instead is with CC. No CDR means permanent stuns/supresses. Lissandra can literally keep you (or herself) in stasis pretty much indefinitely. Amumu can hold your team in place forever. Etc.
No attack speed limit - would be funny to see but I think it'd cause more technical glitches and bugs than anything, just trying to keep up with the animation and registering hits as you start getting 4.0, 5.0 Attacks Per Second.
Run speed.... technically isn't a limit on run speed but there is a soft cap where you start getting a diminished effect on MS after a certain speed. So removing this would let Rammus move EVEN FASTER! but overall wouldn't necessarily change much.
Unique Items being stackable... lol.
x6, deals 48% of your current health on hit.
STACKING BOOTS!
Can't kill me (assuming they don't all proc at once, but take turns) or Tenacity, you are now immune to CC (Hmmm......)
The crit issue isn't a big deal, except for Yasuo. The items with high crit chance like PD don't grant high damage and the damage items don't grant much crit. Even with 6 IE's, you only get 120% crit chance. This would only be a real benefit for Yasuo.