As a point of info, most taxi firms now track arrival times, so quite surprising yours sat and waited. Apologies, of course you had arrived already!

Generally airlines will not cover consequential losses (irritating but thems the rules) and this would be no different for any other carrier. Statutory compensation is calculated on the door opening time, and weather and associated ATC delays don't trigger this anyway. The ground crews would be out of BA's control anyway, at a guess there would have been planes not departing and a lot of stand congestion, so best endeavours will probably have been applied throughout.

I don't really think this is evidence BA aren't what they were (that might be true but it isn't relevant). It's an annoying sequence of events, but these things happen and difficult to see anything that would be done differently by anyone else. The weather over the last few weeks has been pretty dreadful.