I think they did it for investors, not for the sake of regulators. Investors were, I think, beginning to get a little tired of Google's string of goofy product flops — investors wanted Google to focus on what makes it money: ads.
I doubt regulators have ever suggested breaking up a company into a bunch of dependent subsidiaries. There's probably not an office at the DoJ where lawyers are turning over tables and screaming 'you have foiled us again with your restructuring shenanigans, Google'.
I've always been curious about that. Is a parent company + subsidiaries immune from anti-trust laws in the US? I mean, I'm sure Alphabet still shares Google search data across its subsidiaries--which is the real monopoly power concern.
It's probably a lot less about anti-trust and a lot more about bankruptcy protection.
With the companies logically divided, Alphabet can choose devote $XYZ money to some specific initiative and have a guarantee that they're liable for AT MOST that much money. If the sub-company completely mis-manages its assets and goes belly-up, its failure doesn't impact e.g. Google or Waymo (in any deeper way than opportunity cost of the money going to the other sub-company instead of those). Bankruptcy responsibility stops at the owning company and doesn't trickle up to the assets of the company that owns that company, in general.
It's a common pattern for movie studios---Hollywood studios build out a short-lived company to own every film production to insulate themselves from liability and financial disaster.