Point 1 is a good one.
Point 2 about the narrow window... I don't know. We know that there are some people who can deliver good corners/free kicks quite consistently - Gerrard's been doing pretty well for us this season. It stands to reason that effective free kick takers will be tasked to take them more often than not.
I just feel really uncomfortable relying on poor delivery to justify that they aren't much of a threat. I'd imagine that good delivery can be trained quite easily, since it begins from a static position.
But we're not talking about training delivery mate! We're talking about how to improve our corner defending. If a corner is delivered poorly then they wont score now matter how badly you defend (short of conceding a penalty or putting it into your own net). If it's delivered well (which it rarely is because statistically not many corners end up as goals), then there's probably little you can train your defenders to do other than to contest, and have your keeper in the right place.
I think there's enough evidence to corroborate point 2. The fact that many corners are taking short and played deeper in order to get a better angle and pace on the delivery to me suggests that it's difficult to send in a ball from the corner
compared to free kicks or crosses from open play, where there is inherently more variability to how you can deliver the ball. This variability generates a greater degree of uncertainty because the defenders have to prepare for more possible ways that the attacking team can score from such set pieces. In contrast, there's only really a small number of ways an attacking team can deliver a ball from the corner in order to effect a goal. There is less space and angle to work with, there are no offsides so defending teams can just pack the box (hence all the jostling and shoving), and there's less of a concern from a corner taker actually scoring themselves.
I'm not saying it's no risk. But I think the potential reward of lining your lads up and practising thousands of corners, which is time consuming, is probably not all that high. We'd have to look at some stats, but over the course of a season, how many goals from corners can be prevented
from training (NB not simply better defending, players make mistakes all the time despite training every day) - I'd say probably maybe 2-3 goals. Could we use the time to work on things that would save more goals by better use of our midfield, better use of the ball, better passing and better finishing at the other end? I don't know for sure but I'm inclined to think so.
Also worth noting what training would actually constitute. Would it be corner specific tactics, or more generic skills that'll have spin offs elsewhere, like working on players jumping/spring, their balance, stability and flexibility in the air, ability to judge flight etc.
Set pieces, as I said, possibly different story.