They want a celebrity they can shake their fists at and give a right telling off to. Politicians don't build their careers giving tongue-lashings to non-public figures, and that's going to be a problem now.
As I type this, I've just read that Zuckerberg has agreed to testify before a congressional committee - this is going to piss off MPs in the UK all the more though because he snubbed them first (which in turns means whoever gets sent is going to get a lot more abuse and more of the "Where is he!?" feigned outrage).
I'm frankly surprised that Sheryl Sandberg isn't being sent to the UK if Zuckerberg is testifying in the US (although I don't see why he can't do both). The whole angle at the time of her hiring was that she would be "the grown up in the room". I realize that was a long time ago now, but if ever there was a time for the COO to step up this has to be it.
Arguably, that perception is exactly why he has to send a clear subordinate if he isn't going himself, and not someone perceived to be his babysitter.
Cox and Schroepfer both seem more comfortable in front of cameras from what I can find online, and to be honest would probably have better insight into what happened. After all, it's their jobs as the heads of product, and technology.
According to The Guardian, Facebook said that "the company would be putting forward its chief technology officer, Mike Schroepfer, or its chief product officer, Chris Cox."
https://www.theguardian.com/technology/2018/mar/27/facebook-...