So much wrongness.
Let's start with your conclusion, "Canonical doesn't follow the arbitrary pattern I believe I've identified therefore I think it will fail". This isn't science, it's looking for evidence to support your (quite poor) theories.
You started by saying, "businesses that succeed using FOSS". This today covers 95% of successful businesses.
You've ignored the many FOSS-based businesses (those that make and distribute it, not just use it) such as IBM, Amazon, Google, Facebook, Twitter, GitHub. None of these fit your "blessed three" yet they're the dominant model.
And you include "holding out a tin cup" as a successful business strategy. Name a single successful "business" that does this.
Let me explain how successful businesses *really* use FOSS. First, they find a market with incumbents paying too much for their software or spending too much making it. Then they build new FOSS stacks and products that attack these incumbents. They take their clients and charge them a fraction of the old prices. You can sell _anything_ like this, as long as the product has software as part of its critical supply chain.