Yep, I'd seen your earlier post and almsot commented in my broad agreement. I also suspect we've read some of the same articles :)
In the tables I've put up the total number of corners is 8337 with 241 goals scored - a conversion rate of 2.89%. This is a bit lower than your range of 3% to 5% but broadly in the same ballpark and accept totally it depends on the definition of when the corner is over. The figures I'm using are pulled through from sites using OPTA feeds and IIRC their definition is it is a goal within 3 touches of the corner being taken.
I agree to an extent about the barren patches and that was highlighted in no uncertain terms during the "corner counting" sequence last year! City's record of conversion is good as per the tables but perception is skewed because all teams have a low conversion rate. In the example we have failed 671 times out of the 697 corners taken so it is human nature to see the negative from what they consider is repeated failure. This is then probably compounded from the likes of MOTD highlights and seeing a team scoring from a corner.
The inswinging/outgoing debate is another interesting one as well and this was prominent under Mancini as well.
I also think that when this subject is debated fans tend to only remember goals that are scored from headers. I'll bet that when this subject is debated again in a few months, many fans will have subconsciously discounted Yaya's goal. Just as Fernandhino's winner against Villa last season, Kompany's title clincher etc are not taken into account when people discuss the quality of our corners.