Even a 2-3% increase in performance is significant especially when you're playing at the highest level.
It's considered old school because that's the way it's always been done, but as science has improved we've seen significant changes in areas such as diet and conditioning, but when it comes to the time of day that players are training it seems to have stayed the same, well for us atleast.
Now Liverpool are the only team that i'm aware of that train later in the day and they are an incredibly fit team with very few injuries over the course of a season, maybe it isn't the asthma after all?