Yes, but if you're bad at defending both their may be some common reasons. I think we are poor at both, and there are (some) common reasons. We do not appear to be a side that has a clear idea of what it is meant to be doing for set plays, which is an issue for the coaches (who are otherwise doing really, really good things with the club)
Surely then we can simply practise our free kicks defending and see reward with corners at the same time, which is what I was suggesting?
I accept the "low event rate" thing to an extent, but we have conceeded corners in 3 tight games, all of which have cost us points against sides near the top of the table, and went out fo the league cup because of another one. Lukaku's for Everton was simply a really good corner, really well attacked, (though arguably having Glen Johnson marking Lukaku is setting up to fail). The other three had elements of poor defending that can be addressed.
Yes, but this is still very much circumstantial and anecdotal evidence. I think PoP used a good analogy about people being afraid to fly planes because of anecdotal evidence when there's an entire large body of evidence to suggest differently. You can't on the one hand accept that corners are a low rate event in general but for us they aren't (even though the goals we concede from corners are seemingly within acceptable limits as others have pointed out with their percentages) just because of what happened in important games. In fact, if we were to concede from corners at all, those are
exactly the games I would expect to concede in because the top teams have the best players who can deliver well, rather than lower teams who will get fewer corners against us.
I make no secret of the fact that I rated Benitez and his methods very highly. Rodgers' approach is very, very different, and, to be fair, is reaping good results. He has us a far more free flowing, exciting and incisive team in an attacking capacity than Rafa did.
I am a big fan of Rafa's methods. There were many times I thought we played some glorious football with much less capable players.
I'm not suggesting we do no work at all, but I think you have to pick your battles. I think we had a massive problem with scoring goals and we've largely addressed that and still have some way to go I feel. In the mean time I'm pretty happy to be a bit suspect on corners if it means we'll not concede from open play, and score a few more at the other end. It would really depend on how many goals the training staff thought we could prevent. Without knowing how much they even practise corners, it's hard to comment on that.
Free kicks, which I think are a different kettle of fish, is a different story. It may be as you say that there are some common skills that we need to work on like our jumping, positioning, balance, coordination, timing etc. but I would preferentially concentrate on our set pieces (where I don't think we have any system) rather than corners, where we aren't the best but we really aren't too bad.