Incidentally, that would put the number around the 70 quoted in the grandparent comment.
My guess is salespeople would utilize most of their attention externally. Perhaps junior engineers internally? (This could also explain why it's economical for companies to pay for dinner and sponsor happy hours)
Another area that organizations struggle with is spending the time to put the structure in. They may say, "It takes more effort to put in structure, so while we want to be structured, let's just work harder as we go from 150 to 250, we'll solve it later when we're less busy" Then it goes from 250 to 400, then the next thing you know it's a 1600 person mess. :-)
I don't know if it's even possible, but why not push a small group to become owners of their own shop, outsourcing work to them ? This might push those small groups to seek other connections to the external world and thus build strength and resiliency.
Of course this implies giving up the money. This is probably where the core tension lies. I guess many wouldn't even want to think about it.
Semco (quoted elsewhere) was big on the "fund your best people's ideas" concept to cut loose companies. When you have to get external funding too, it forces discipline. The kerietsu (sp?) concept breaks down during tough times when partial owners subsidize the weaker units in the group. This happened in Japan.
This isn't a simple problem, because there's no one size fits all solution.
There is structure, and there are explicit rules for how that structure is modified. There are rules that require decision making to be documented rather than held in your brain. Accountability is explicit. The entire system is designed to be scalable by a process that allows individual roles to transition to teams (or back) with as much nesting is required for the business at hand. On the whole the design is aggressive about making things explicit and systematized.
Whether it works or not I don't know, but it's clearly not the kind of free for all you're assuming.
Valve, of course is the most well-known, but Semco is a large brazilian company that runs this way, as is Morning Star, a tomato processing company in California.
A browse through Morning Star's website reveals job listings for defined roles. They're looking for (i) people with "a strong business background" and "an aspiration for senior leadership" to manage their finances, (ii) people who "likely have a meaningful formal education in related disciplines" to "coordinate", "train" and "identify proper operating procedures", and (iii) "hands on professionals" who need the "ability to read, write, and comprehend instructions" in addition to specific practical skills.
Sure, they might downplay rank and authority, but it doesn't sound like an organization without structure or de facto managerial roles.
I'm curious because models that work in good times don't always work in tough times.