Investing legend Bill Miller says it's 'insane' for Twitter to have a part-time CEO

Jack Dorsey, Twitter and Square founder, in a London cafe

"If a part-time CEO makes sense, then so does a part-time CFO, part-time chief technology officer," Bill Miller said.

While Twitter is a "unique asset," legendary investor Bill Miller said the company needs a full-time CEO.

"It is insane to have Jack Dorsey be a part-time CEO at a company with the issues that Twitter has," Miller said in an interview with CNBC's Scott Wapner on " Halftime Report " on Monday. "If a part-time CEO makes sense, then so does a part-time CFO, part-time chief technology officer. That just makes no sense whatsoever."

For example, Miller said that the company could simply charge the companies that use Twitter as a customer service platform. Even if Twitter loses users while overhauling its business model, Miller said the company could see see millions in free cash flow a month just by charging $1 a month for the service on remaining users.

Miller's firm recently sold half of its call options in Twitter, he said.

Amazon actually isn't as "terribly expensive" as some investors think, Miller said. Analysts project the online retail giant's enterprise value-to-EBITDA to be about 12.5 for fiscal 2018, according to a FactSet consensus estimate. Miller said that figure is a "crazy low number."

Miller previously said in September at the Delivering Alpha conference sponsored by CNBC and Institutional Investor that the stock could double in three years .

Amazon CEO Jeff Bezos is an "authentic business genius," Miller said. Compared to other great companies like Facebook or Google's parent company Alphabet , Miller said Amazon's total addressable market is "just so much bigger than basically any other company on earth right now."

"Facebook and Google, in their core business, are attacking the global ad market. That's where most of their revenues are coming from. That's a $500 billion market," Miller said. "Amazon's core market, retail in the U.S. alone, is $5 trillion.