Warks, I suppose it can depend on whether you are travelling for business or leisure.
Most leisure travellers look for the cheapest deal and fail to take the time to understand the rules of the fare they have bought. When they run late (regardless of the reason), they blame the airline, rant and rave and say "I'll never fly with this airline again" - you've seen the type of people on various Airline reality shows.
Some (if not most) business travellers will, because of experience, pay more for the flexibility that a higher fare basis carries. I always look at flying to destinations the night before (generally on a V class fare), to reduce the risks of unserviceable aircraft or weather conditions that might happen at short notice and not allow me to reschedule without losing face with my clients.
On my return flights (usually mid to late afternoon and into early evening), I need flexibility thus I am always on a K class fare or sometimes H. This allows me the flexibility to change at short notice, as there are generally seats available on later flights at these fares (thus no change fee). A case in point (like your example), was my return flight SYD/BNE on Friday - I had initially bought a K class for Thursday PM return, then changed to a Friday PM return and had to go up to H class (an extra $100) to get on the [later] 3.05pm flight. I was at Parramatta and left my clients at 1pm to catch the train via Central to the Airport. We were stopped at Auburn due to an accident between a train and pedestrian. Rather than tempt fate, I rang QF Res from the train by mobile, explained my position and asked the CSA to look for later flights with H availability. The 4.05pm had only J seats available, luckily the 5.05pm had H availability. Imagine if I had been on a cheaper fare - there would not have been a snowflakes chance of getting out of SYD on a Friday afternoon (as the CSA was telling me what fares were available - it would not have been until 8.05pm that a K class would have secured me a seat).