To stretch the car analogies, perhaps torturously…
It seems to me wordpress.com is the "we supply the racing car and driver" solution provider. You don't have to worry about how it gets driven, but you also have only limited say in what car you get and which lines the driver takes through corners.
In my version, WPEngine are providing the race track - to which you bring your own car and driver. They go to a bit of effort to improve the safety, mostly by ensuring other track users don't do too much to affect your performance, but you're free to bring your own F1 car, MotoGP motorcycle, Nascar, or go kart; and run at whatever pace you think is appropriate.
Seems to me the OP's problem was that he wanted to run a top fuel drag rail. From his perspective, he made assumptions about what "a race track" meant that didn't include "decreasing radius downhill hairpins". Meanwhile WPEngine's website/marketing didn't anticipate that class of user, and didn't think they needed to point out that their track isn't an ANDRA approved 1440' long straight with a mile or two of slightly uphill runoff at the end.
With my sympathetic hat on, I can easily understand why both parties assumptions were sensible to them when they made them.
With my cynical hat on, it's pretty obvious that you could install a Wordpress theme or plugin on anybodies hosting platform with an O(m^n) or O(n!) function it it somewhere, and no magical cloud autoscaling pixiedust is going to solve your problem. At the same time, the expectation that a company claiming "Insanely Fast. Infinitely Scalable." and "At WP Engine, there’s no “first level” of support–our entire staff are WordPress experts, so you never hear “We don’t know how to do that.”" on their homepage should be able to do a better job keeping a Wordpress site up than some time-limited non-technical guy self-hosting on Linode.