We always arrive at the airport with plenty of time to spare.
We did, however, once almost miss a flight once already through security and in the departure lounge through no fault of our own. A fire alarm had gone off down the corridor that led to the gate so we and all other passengers were prevented from going down there.
You'd have thought that the airline (Ryanair!!) would have accepted that they would have to wait, but no! They were jumping up and down giving off about how late we all were and how Ryanair would be going anyway in order to stay on schedule, even though no passengers would have been on board! In the end they did back down and we were allowed to board, but they were twatty about it. That flight, along with others departing from neighbouring gates, was delayed by about half an hour.
Regarding the luggage being tagged to the passenger, yes it is, but the system doesn't always work perfectly. We were once already boarded on our flight (Ryanair again!!) and there seemed to be about a 30 minute delay leaving the gate for some reason. We'd gone through all the checkpoints and security with no problems at all and our boarding passes definitely showed what checked hold baggage we were travelling with.
It wasn't until we had landed at our destination airport in Spain and were standing like a pair of lemons at the baggage carousel that we realised our case wasn't coming out. Airline staff there made a call back to Stansted and it turned out that they had been offloading our luggage while we were actually on board. Cabin staff had not put out any calls asking for "passengers by the name of Mr. & Mrs. Topseyt please make yourselves known to cabin staff" as they should have done. That would have answered the question in about 30 seconds, but maybe that is too simple for them. Instead, unknown to us, they offloaded the case, which took quite a while and caused a needless delay.
We did get compensation for that. Ryanair was forced to fly the case out on the very next flight and courier it to us at our hotel.