I don't think there was ever one crew on a commercial airliner who overran the runway because they had not computed the perfs.
I am going to check as many overruns reports as I can, but from my memory, the vast majority happened not because of an insufficient TODA in itself, but because the approach or the landing or the braking, or several combined, were not conducted in a satisfactory manner.
Let's start :
Southwest 1248 : lack of familiarity with the autobrake system leading to a very delayed use of the reversers
Hawaian airlines 481 at Tahiti : landing inside a thunderstorm with a delay in the use of spoilers
AF 072 (nicknamed "the GITANIC") : landing with power on one engine out of 4
TAM 3054 : landing with full power on one engine out of 2
AF 358 at Toronto : the runway was sufficient, but the problem boiled down to landing and braking technique.
American 1420 at Little rock : landing in a thunderstorm
B747 Qantas 1 : go around initiated but aborted, then reverse thrust not used, one engine left at TOGA
This report also says that the majority of overruns happen when the runway is wet or worse, and when the airplane energy is too high during approach.
Air india 1344 : long landing, flooded runway
Pegasus 2193 : inadequate braking technique, excessive energy on final
Saha Airlines : they got confused and landed on the wrong runway, which was much shorter. No doubt the perfs calculations were perfect for the intended runway.
Skylease cargo 4854 : inadequate braking technique
I am not going to look at the entire list of runway excursions that are listed on wikipedia, I did not find one occurence where the crew elected to land on a runway that was too short. Not one. If you find at least one, please point it out. All occurences were due to an improper flying or braking technique.
Even if a crew overran a runway because of an insufficient distance (with a correct landing and braking technique), without having calculated the perfs, the fault would still reside in the failure to identify the factors leading a runway that is usually enough to be insufficient that day.
Because if a crew does not recognize the factors leading to an increased landing distance (slipperyness, aircraft failures, tailwind, ..) there is a chance they would have ignored that factor too during the perf calculation.
In my opinion, having a rule of thumb is necessary to fully understand what we're doing, as well as understanding all the assumptions. The manufacturer should provide it (still an opinion), but they don't, maybe because they think it would encourage "complacency" (even though it would not). I prefer to fly with a captain who won't compute anything the 999 times that he's sure it's not necessary, and does it the 1 time that it is required, rather than a captain who will compute everything the 999 times, and not do it the 1 time that he needed to, or miss that time an important element that lead to a stopping distance issue. Or that does everything correctly until the moment he lines up on the wrong, shorter runway.
Saying that if I "ignore" that procedure (it's a tough call to say I'm ignoring it when I'm writing literaly pages about it), makes you wonder about what other procedures I would ignore, is a slippery slope argument. You can conclude by yourself what type of rules I "ignore" : the ones that don't have a rational basis. For example at my airline we have a double sided bus station. One side goes from the security control to the car park, and the other side goes from the security control to the planes. On one side, the high vis jacket is required, as if we were already on the planes parking. On the other side, nothing is required. But both sides strictly resemble a normal street with buses, sidewalks.. This rule is enforced by fines up to 1000 bucks, which is why I don't "ignore" it, but I can argue that this is stupid.
There are very few rules that are stupid (lack rational basis) in the airlines. (Most of them are found at security checks on the ground, imo)
And on this topic, the regulation seems to confirm my arguing because the perfs calculation isn't mandatory in flight, as cited above. As long as the crew has evaluated the situation, the AMC (which not the same level of regulation as a law) allows not to redo it.
To me, this debate sounds like an issue of skills vs legal covering. But you don't need to be covered legally if you know what you're talking about.
In my experience of 2000 hours until now, I have observed a pattern that the most confident captains, who put the airplane in an undesired state the least often, tend to apply the rules with more analysis and common sense, whereas the least confident ones, who know they are more prone of causing an undesired state, will make more cautious decisions in order to be "covered". For example I remember a captain who stopped the airplane mid-taxi because he was informed by ATC that some taxiway lights were missing. At an airfield that we practised several times per week, and during a night with very good visibility and fully functionning aircraft lights. We ended up finding that... there is no clear rule in our ops manual as to which taxiway lights are required to taxi at night !
So yes, long story short, if you feel the need to add 5 knots on final, do it. (But if you're landing a heavy 319/320 at the wet Firenze (LIRQ) runway with tailwind, don't do it)
The takeoff perf matter is very different in my opinion. You can takeoff with a wide variety of takeoff mass, especially on a long haul plane. And the goal is to optimize the flex temperature, so for that obviously you need the computer.
But then again, let's take a step back. Have you noticed that the flysmart app will give you higher Vr for the same mass if you choose a longer runway ? That means that you could rotate lift off before the computed Vr and the airplane would fly normally, only in a less optimized manner. As long as you're above the real minimum Vr. I found cases with up to 30 knots difference between the minimum Vr and computed Vr, for the same conditions except departure intersection.
The incidents and accidents that happened during the takeoff phase due to incorrect calculations only concerned the most severe mistakes. Flap setting and gross errors regarding the mass. Overlooking icing. Wrong aircraft or engine type... Much of the rest is negligible.. We still input all the parameters to save a little bit of money.