This is an interesting post. While I have no knowledge of Barcelona it does seem that the hotel could take some measures to alleviate the problem.
The first issue seems to be that taxis are reluctant to go to the hotel. The hotel should be taking some action with taxis or the relevant authority to ensure that taxis are available for guests.
If issues were anticipated for NYD it would have been courteous to advise guests in advance of this eventuality.
Hotel comments on the day that getting a taxi was not possible as it was a holiday seem to have been proved to be untrue, given that OP found a taxi, and taxis were available in the city.
In addition websites indicate that taxis can be ordered by phone in Barcelona.
Could not the hotel have tried phoning and ordering taxis?