Large companies, even monopolies, aren't the problem. Unfair leverage to suppress competition is. Those products without the subsidizing revenue of ads, and ads without the information flows of those products, is the goal.

Who gets what part of the company is the wrong question to ask. The org chart would get split along those business units. In all likelihood, the company called "Google" would be the software side, since that's where search lives.

They are a problem in terms of an efficient free market; they make the information flow asymmetrically biased in their favor, and cause higher prices and implicit collusion. That is true even without any intent to harm.