I did a little searching (I'm NOT a lawyer) and couldn't come up with anything that would explicitly prohibit a company from operating as both in the USA or the EU -- but I'm definitely not authoritative on that.
The definitions are a little fuzzy: airline can mean a few different things in a strict legal sense: there's a big difference between someone flying a few tourists around compared to British Airways or United carrying millions of people. If I can get a type certificate / approval and build an airplane, that makes me a manufacturer. If I then charge people for transportation, I can at least argue that makes me an airline, right?
With that said, like a lot of aviation (particularly airline) questions, I think you'll find that the answer is more tightly coupled to economics than it is law or physics...
Running an "airline" in the conventional sense of the term is an incredibly expensive, high-risk, high-capital, complex operation. Billions of dollars in investment has been poured into that industry over decades, and a large percentage of it has been lost. To be competitive in this space requires extremely specific business skills that are hard to find in general, and even harder to retain.
Running an aircraft manufacturing operation is also very complex, highly-regulated (in lots of different ways) and also requires a set of business, technology, and people resources that are ALSO really really hard to find and keep. There probably aren't more than a dozen "large" aircraft manufacturing operations in the world today, only a handful are in the business of "building airplanes for airlines" in the traditional definitions, and the costs are a huge part of why that's the case. (See also: the exceptional consolidation of both airlines and manufacturers in the last few decades)
For your examples, for Boeing to try and operate as an airline would come with some economies of scale (they'd be buying their own airplanes, right?) but would also come with massive additional costs and complexities -- one of the largest being the business problem that they'd be "competing with their own customer base": this is never a fun place for a for-profit enterprise to land.
I was able to come up with only two scenarios where this might happen:
- something like where a "crazed genius billionaire" (Think Richard Branson or Elon Musk or Jeff Bezos?) just decides they want to do both and can put up the monstrous capital required to try.
- A nation-state decides that it's in their national interest to have both a major manufacturer and a national airline, and is willing to fund such an investment. There are certainly arguments that many large airlines and most if not all large manufacturers are the recipients of government support already (though the extent of this and the legality is VERY hotly debated) - so this would also sort of straddle the fence between what is a "company" and what is a "government".