Both your argument and the ones of the IAA have logic. Yes itts true the coins could have rolled into the mud and found its way down there especially considering that they didn't exactly keep the place clean and tidy for tourists back then. It is also possible though that Herod started the building and it was finished by his grandson the Kotel is just an outer wall of the basic Temple area complex and had no holy significance back then so I think its possible that the complex was built with priorities Temple, walls closet to the Temple and further out etc in which case it could have taken a very long time for them to get round to the Western Wall. If it was built with priorities on which areas were most important I doubt the Kotel would have been very high on the list because there was nothing holy about it and the thing is far from where the main Temple would have been. Idon't think that it matters though at the end of the day if the thing was finished by Herod or his grandson the thing was still built in the same basic time frame might have just taken a few years longer than originally thought.
Palestinian wounded in clashes with Israeli forces two days ago succumbs to wounds (Haaretz)