On Wednesday, activist investor Nelson Peltz floated a splashy plan for PepsiCo: Buy Oreo-maker Mondelez to form a "global snack leader," while spinning off the beverage business entirely. He owns about $1.3 billion in PepsiCo's stock, or about 1 percent of the company, which means his words carry some weight--and he's forced other companies to shift their strategies before.

PepsiCo has indicated it isn't planning to take Peltz up on his idea. But his reasoning, which his company Trian outlined in a 59-page public white paper, is itself an interesting window into a massive corporation that holds a lot of influence over how we eat.  Here are a few takeaways:

Regular Pepsi is still by far PepsiCo's biggest revenue generator. 

Despite moves into healthier beverages--following the public's move away from sugary drinks--PepsiCo still makes most of its money on the stuff that's bad for you. That shows why it's hard for food companies to shift in more healthy directions: Shareholders see where the money's coming from, and don't want to mess with success.

Trian writes that PepsiCo's bid to build a $30 billion nutrition business has been a "distraction." "The focus on NutritionCo also led to a perception that management had disavowed its 'fun for you' portfolio – the heart of PepsiCo’s business," it says.

The downside of consolidation: Snacks and beverages don't always get along.

Thus far, PepsiCo has adhered to a strategy it calls the "Power of One," which leverages the fact that snacks and drinks are often consumed together. But Trian thinks that in reality, PepsiCo's flagging beverage business is dragging down the snack side, in part because analysts still think of it it as a beverage company rather than a diversified food company, and also because they require different management strategies. Right now, Trian says, there is a "dominance of snack minded management in charge of execution."

"There is a risk that bright beverage executives at PepsiCo may be concerned by what we externally see as a subjugation of the beverage unit’s culture and needs to Frito Lay," Trian writes. "The unintended message that may be getting sent by the recent management moves and by the snack heavy senior leadership is that any talented individual who wants to rise through the beverage ranks must flow through the food business at some point. There seems to be little room and hope for native and career beverage executives at PepsiCo.”

Advertising still matters. 

Coke is king, Trian suggests, not just because it's a pure play beverage company--it also spends a lot on advertising to maintain its primacy in the American imagination.

Investors use markets to set the stage for their own ideas.

Trian's paper included a slide illustrating how share prices jumped after a rumor about a potential PepsiCo acquisition of Mondelez surfaced in March--which it may have floated to strategically bolster its argument a few months later.

Do companies really compete when the same people own most of them? 

Part of the reason a PepsiCo acquisition of Mondelez makes sense to Trian is that it already owns significant chunks of both of them--as do most of PepsiCo's top shareholders. Corporate consolidation is only one element of the overlapping ownership of America's biggest industries.