As far as I'm aware, Firefox is the browser engine they contribute least to: they have many more clients who have much more interest in WebKit or Chromium based browsers and that's where the majority of work goes.
You mentioned Canonical and Red hat IBM. For Canonical I actually don't know their model (they had Amazon search integrated but haven't seen them in any business context) RedHat (now IBM) has servicesl/support.
For other I see with notable scale
- MySQL (nowadays Oracle) with services/support and dual licensing - Qt (Trolltech/Nokia/Digi/Qt Company) with dial licensing and consulting services -MongoDB, Redis, ElasticLabs all burning VC and support, dual licensing
After those the list becomes short for me. Most other open source software is side business, from doing something else (i.e. many Apache or Eclipse projects) or supported by small companies/individual developers who do consulting around it or got sometime from their employer to work on it. - npm: burning VC (and offering commercial repo) (now GitHub/Microsoft not sure they want to see profits from it or only control of the environment)
Most successful "open source" companies use an open core model, where they provide services and proprietary add-ons related to an open source project that they contribute to but may not actually own. Think GitHub or Docker.
Blender is a much more successful example (and there was another open source project here on HN with $300k income where companies could pay for features to be implemented, but still not company specific).
1.) Many of the companies that make the most on open source are not software vendors per se but still significant contributors in their own right. Example: Google, Facebook. Kubernetes exists because of Google. Facebook has a ridiculously long list of significant projects. [1] It's really important not to ignore this because you are otherwise missing the core economics of the open source movement.
2. There are lots of companies making good money operating open source in the cloud. Data Bricks, Confluent, MongoDB, and Amazon (specifically Aurora) are good examples. I'm not saying the companies are necessarily all profitable, only that their COGS look good and they will be profitable in due time. The key is you need to have software that is worth paying other people to operate. Data management is common to many of the main contenders.
Mozilla's problem is they aren't #1 and don't offer software that would allow them to become #2.
The problem is Edge and Chrome are free already so charging for a compiled browser is probably not going to work