OP's "extra reads" is dumb because he could have had normal metrics for memcached load and planned to only support like 70% capacity or somesuch, and when load hit that number, he would immediately increase capacity. Instead he's running with a handicap. It's just useless.
Secondly, you should know what your capacity is. Stress testing exists for a reason.
Stress-testing, shared-nothing and dollar-scalable are platonic ideals, and they're not always achievable. If Dropbox had three infrastructure engineers, they probably weren't able to build proper capacity planning models, and probably couldn't afford to build a full production work-alike for stress testing anyway. (And at some scales, that's literally impossible. Our vendors couldn't physically manufacture enough servers to build a full test environment, cost aside.) I'm sure they did some simulated tests as well, but those won't tell you the whole story.
You're focused on IOPS, but you have no idea if that's what Dropbox's bottlenecks were. (Not to mention: What does IOPS mean on an EBS and S3 infrastructure?) Complex systems fall over in complex ways. You can predict the next bottleneck, but not the one after that; by the time you get there, your fix for the first bottleneck will have changed the dynamics.
It sounds like they did do stress testing, using real-world loads, on a system that was 100% similar to their production system. They ran continuous just-in-time stress tests in the Big Lab.
That being said, trends in user visits are of course great numbers for capacity planning because you have an idea how much growth to expect in the near future. But it's only a vague multiplier; you need to know how beefy a box to get (by stress testing to determine capacity) and then multiply by the growth factor. But it's usually more complicated than this.
Stress testing doesn't have to be a formal process in all environments. You might just have a developer with a new chat server and they want to get a benchmark of how many users can join and chat before CPU peaks. An hour or two of coding should provide a workable test on like-hardware, which can then be generalized with tests of other software to give an idea of the capacity when a certain number of users are logged in and performing the same operations. The point isn't to know 100% when you will fall over, but to have at least an idea when you're going to fall over, so you don't have to actually fall over to figure out when and where to scale.
I have no problems with very-short-term big lab stress testing. We had the same issue at my last place, and with lots of caution, it worked fine. But jesus christ, if I told my bosses "I think we should run all the servers with extra load until they fall over, then re-evaluate", they'd look at me like I had antlers growing out of my head.
Incidentally, fuel dump systems were initially added due to a rule by the FAA that a plane's structural landing weight not be exceeded by its takeoff weight. Many commercial planes never had this problem, so dumping systems were not installed. As a result, most planes just circle until they've burned up enough fuel, or land anyway overweight. You could dump fuel to lessen the chance of explosion, but only if your plane is equipped with a fuel dump system, and such incidents are so rare it's not even a safety consideration.
"Why not just plan ahead? Because most of the time, it was a very abrupt failure that we couldn’t detect with monitoring."
So you have a system, and you have monitoring in place. Let's say the monitors were set up for 1 minute polls, because somebody thought that was a good idea. Suddenly you find out one of your servers is down. Oh noes! There's 45 seconds until the monitor finds this out, which would be horrible.
Since we have doubled the reads on the existing servers, we now no longer have capacity and connections are stacking up. Shit :'( But not to worry! Let's just quickly kill the extra reads - now we have more capacity! Hooray!
Except, if the extra reads weren't happening, they would have already had extra fucking capacity and not had to flip a switch in the first place.
Now you see why i'm mad, bro?
They actually do this kind of stuff (except for the "lets dump the lead" part), in stress tests, especially in cargo and millitary planes. And they do similar tests not only in aviation, but in most kinds of engineering.
So maybe misplaced sarcasm?