What are the reasons for using a cradle with a handlebar mounted drybag?
Having now toured for two weeks using a dry bag strapped directly to my own handlebars, I can now sort of answer this question. I still haven't toured with a cradle, so I can't give a full side-by side comparison, but I can say that I spent two weeks riding without one and I didn't particularly miss having a crade. All of the comments by u02sgb in their answer seem potentially valid – I can imagine maybe it being more stable or easier to attach (edit: mostly easier to attach, stability was fine) – but those seem more nice-to-have than a must-have. 

The main reason I can think of where it might become more of a must-have is if you were going to be on a multi-month tour, you might want one to prevent bag wear; I noticed some wear to my drybag where the straps went. Not a lot, the bag is far from worn out after two weeks, but it probably would wear out faster than a drybag would ordinarily. One could probably also mitigate that by getting a drybag that has reinforced tiedown points, or some other scheme to protect the bag from the strap (a wider strap, or a strap through a bit of used firehose perhaps).