Who is responsible for the check-in queues?

Few days ago I had a reservation for a flight in Switzerland with luggage and a departure time 2pm. When I checked in online I saw that the flight is delayed around an hour. When I arrived at the airport around 1pm, it turned out that there was a terrible queue at the check-in desks, so I went to the priority boarding queue and told the lady that my flight is shortly. She sent me to the customer service to buy the priority boarding. There was another queue there, so after a visit there and using priority boarding I arrived at the check-in desk at 2pm. The assistant there told me that it's too late for me to drop my bag, as the cutoff time set by the airline - 40min before departure counts from the original departure time, and that I'll not be able to fly that day (plane was leaving an hour later).

Is it really me who is responsible for getting in front of the queue? Could this be a good ground for compensation claim, eg ec261 (I was at the check-in desk in time, but was not served promptly due to the queue)? Tldr facts:
- I joined the check-in queue around 60 min before the scheduled departure time
- I was at the desk an hour before the actual departure
- the luggage drop time was marked on boarding pass as "40 min before departure", but on the terms of service as "before the scheduled time of departure"
If it is the airline who is responsible for making queues short enough, can I sue in a different country than departure/arrival?
If it is mine responsibility, is there an insurance I could buy that could cover that? I was looking for the offers, but it seems all of them allow to cancel only a couple of days before the flight or in case of some sickness.

Thank you for the answers and sorry for multiple questions, I wanted to provide the common context once.

Best Answer

The original scheduled departure time sets the clock for check in and baggage drop times. The fact that the flight is delayed does not change the pre-flight procedures for passengers. And your arriving only 20 minutes prior to the scheduled cut off for check in does not place any additional responsibility on the airline to process you quicker.

Most airlines tell passengers to arrive 2 to 3 hours ahead of departure (depending on airport and destination) for the simple reason there will be lines checking in and clearing security.

Airlines schedule staffing for check in counters based on past needs, finding a balance between accommodating the crowds and not being overstaffed. They can't magically find extra workers if the line gets unexpectedly long (and most of us don't want to pay higher airfares simply to have extra staff sitting around waiting for unprepared travelers).

Some airlines, as a public relations measure, will do a bit extra to accommodate late arriving check ins, but they are not legally obligated to do so. The passengers bear the burden of responsibility to be prepared for their trip, which includes getting to the airport in a timely fashion.