Why can't some chieftains learn? Last week, speaking before Showtime Arabia in Dubai, Viacom (NYSE:VIA) CEO Sumner Redstone indicated that the media conglomerate's amusement park and publishing businesses were on the block.

"We have certain assets which give us a lot of cash flow but don't have the growth potential that we are looking for, like the theme parks and Simon & Schuster," he was quoted as saying to the executives and journalists in attendance. ''If someone offered us enough money, we would probably sell."

I think selling off its book business would be a shame, but I understand the company's need to unlock shareholder value in its non-core assets. However, I think unloading its amusement parks would be a colossal mistake at just about any price.

I felt that way earlier this year, when the company first floated the idea of dumping its Paramount Parks chain. The four domestic parks and a fifth gated attraction in Canada draw roughly 10 million guests a year. Imagine an entertainment company giving up its claim on a captive audience that large. Ludicrous, isn't it?

Cedar Fair (NYSE:FUN) doesn't have movies or cartoon channels to plug, yet it still carves out a beautiful business. That company's earnings consistency and its knack for raising its annual unit distributions have made it an Income Investor natural. Six Flags (NYSE:PKS) is also far removed from when it was a Time Warner (NYSE:TWX) property, yet when it put itself up on the block, it was greeted with a lack of interested buyers.

Because Viacom has valuable entertainment assets in its hands, amusement parks make even more sense for the company than they do to traditional operators. Ask Disney (NYSE:DIS) or General Electric's (NYSE:GE) Universal how important it is to have their global theme parks when it comes time to market their latest flicks. Even Inside Value pick Anheuser-Busch (NYSE:BUD) owns a series of parks for the sake of brand ambassadorship, above and beyond the tempting cash flow.

Amusement parks are often seen as a regional outing for kids, teens, and young families, and Viacom targets those groups around the clock at MTV, Nickelodeon, and CBS. Parks are a logical connection, and one has to wonder why Viacom would be willing to snip the string that connects the Dixie cups.

Cashing out of the amusement park business becomes an even more stupefying option when one realizes that Viacom is also a major player in billboard advertising and radio. How can a company that clearly understands the value of drifting eyeballs on heavily trafficked roadways not make the most of 10 million annual guests that they will own for hours at a time?

What's more, parks are sensory experiences, so why isn't more of Viacom's Infinity Broadcasting content and televised material being made available to folks waiting in line on rides?

Is Redstone's biggest mistake putting the park chain up for sale or failing to maximize the obvious synergies? It doesn't matter. A buyer at an attractive price is unlikely at this point, because the ideal owner just happens to be the company that owns it already.

Poor Viacom. In its rush to split, it seems to have lopped off a good chunk of common sense. Let's hope it grows back.

Time Warner is a Motley Fool Stock Advisor recommendation.

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Longtime Fool contributor Rick Munarriz enjoys taking his family on coaster treks over the summer. He owns shares in Disney and units in Cedar Fair. The Fool has a disclosure policy. He is also part of theRule Breakersnewsletter research team, seeking out tomorrow's ultimate growth stocks a day early.