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In the old days a cargo ship or bulk liquids carrier would have it's own means (manpower then derricks / pumps) to be able to offload cargo itself, as long as they could get alongside something suitable (or something smaller get alongside them).
Whilst I assume there must be floating cranes tall enough(?) to reach the topmost containers on Ever Given, she likely to be sitting even higher in the water than 'normal', given she's aground both bow and stern.
They then have to put (enough of) them somewhere and that's not easy in that narrow canal.
Plus, floating cranes that big are probably few and far between and not known to be particularly fast, especially on the high seas and if they have to come a long way.
It is a mess indeed. ;-(
Cheers, T i m