I don't know...it seems to work pretty well for Valve who's scaled it up to about 300 last I looked.
Granted, not everyone is fit for such a culture, and there are plenty of "It ain't all chocolate and roses at Valve!" stories to attest to that. But lets face it, most humans really are happiest following, what's left is happiest leading. The percentage of humans who can be happy in a peer culture, especially when those peers are all high achievers, is honestly so small it's not much more than statistical noise.
So to that sense you're right: Few companies are able to scale with a flat model simply because the available pool of suitable talent for such an organization is so incredibly small. Couple that intrinsic soft cap on scale with the fact that "bad seeds" can do a very disproportionate amount of harm to such organization structures...and the larger your organization, the higher the likelihood that a bad seed will slip in. So that creates another soft-cap: As the organization scales, so must the strictness of the screening process for new highers. Eventually it'll just choke itself off, unable to grow.
That choke point however, I'd argue is dramatically higher than you've suggested.