Re: Crits
In practice I rarely see a table use RAW crits. It's usually the first thing house ruled. They have to put something in the book. As far as the current iteration "taking longer"...1 out of every 20 attacks requiring another roll isn't much of a time sink IMO.
Re: Cover
IIRC Barbarians will have advantage when raging. Raging Barbarians would ignore cover if the adv/dis mechanic is used. They may be fine for some, but there are other cases, I forget (Was it rogue/assassin stuff?), that are similar to this. By going to a penalty it eliminates the strangeness that came up in playtests. I think cover as a penalty is one of those cases where playtest feedback determined the basic rule.
if you use disadvantage and full cover (3/4 cover) remember that Adv/Dis is effectively a sliding scale (ie adv when you need a Nat 20 to hit is effectively a +0.5 bonus where adv when you need a Nat 10 to hit is effectively a +5 bonus). A full plate wearing fighter behind an arrow slit is effectively AC 23 with RAW...but using Dis means an effective AC 20 which is easier to hit. A guy not wearing armor behind an arrow slit is just as easy to hit using a -5 penalty (+5 AC) or Disadvantage. Now add a rogues first strike ability which grants adv, and suddenly the arrow slit is not effective at all! Strangeness...
But do what floats your boat. Your Game, Your Way.