AFAIK, Mozilla has the structure they do because the IRS frowns upon charities (which is shorthand for "tax-exempt corporation") engaging in business-like activities but is fine with charities owning for-profit companies as a source of income (and like any shareholder can do, direct the for-profit company to benefit its owner).

Regional differences may be relevant here: in Canada, you can incorporate a nonprofit corporation and later apply for charity status (which restricts the company's possible activities in exchange for a 0% income tax rate) but it's completely optional.

In the US, on the other hand, to the best of my knowledge, one has to establish a for-profit entity first and then apply to the IRS to recognize it as a charity (which is a lengthy process). The words "charity" and "nonprofit" are interchangeable in the US for that reason.

If the concept of a non-charitable nonprofit exists in your jurisdiction, you can get the benefits of a nonprofit structure (ie. no owners) without restricting the company's activities, minus tax exemption and being able to issue tax receipts.

For context: I founded a non-charitable nonprofit in Canada; I'm not super familiar with the US side of things so I'm happy to be corrected.