You can write any license you want and claim it's an open source license. It won't be OSI approved of course and, you almost certainly won't build a meaningful community around it but there's nothing keeping you from creating one.
Many big companies (especially vendors) do contribute with people and otherwise--because, as you say, it does often help themselves--and most significant developers of major open source projects are doing it as part of their day job.
There's a long history of licenses in the PC freeware/shareware space of being only for personal use/educational use/etc. That usage-based restrictions did not make it into the FOSS world is an important reason that it's been so successful IMO.
I hate to be flippant, but that's a well-known business model called "contracting". It's possible, absolutely, but it requires a substantial investment of time and effort in business concerns on top of the actual software development. In practice, most leaders of contracting businesses don't have time to write code, and most contracting businesses end up deciding they need to release closed-source extensions.
As far as I know Mozilla doesn't sell any software licenses. They were almost entirely subsidized by Netscape from 1998 to 2003, then by Google from 2005 to 2014, and by a variety of search engines competing for Firefox default status since then. That kind of "cash cow" model gives you a lot more organizational freedom than software licensing.
And why would you compare it to a regular software "vendor" when it produces free open software for 99.9% of the people, and non-free open software for 0.1% which are large corporations?
