Your theory doesn't match the timeline. Under the engineering first strategy, Google became the juggernaut it is today, with products like Gmail, Maps, Street View and of course Search.
Unfortunately, the approach doesn't work for all product categories. Product design, usability, simplicity, and sheer style were not the forte of the Google of old. As a result they saw themselves fall behind Facebook in social, failed to stop the tsunami that was iPhone, could not compete with Amazon in e-commerce, and ceded heavy ground to it in home automation.
But Google still wanted these things and more, as all exceptionalist mega corps do. So they did the unthinkable. They handed the decision making back to the same product and business overlords that they had once shunned.
As someone who has one foot in engineering and one foot in product design, I know how important product experts are in producing well loved, intuitive, and incredibly successful experiences at scale. However, you can feel it in the experience as a user when the product team is given the keys to the kingdom and left unchallenged. The product becomes soulless and vapid. It loses it's charm and abandons it's loyal customers when the wind shifts even slightly.
I'm not placing the blame solely on Google's product apparatus, quite the opposite. It's clear that it's engineering apparatus has become so careless, so content with the status quo and the cushy paycheck and perks, that they don't push back anymore. Whenever you use a Google product as a software engineer and you wonder how it's possible that its blatantly obvious failures made it one day in the dev process of a company that apparently prides itself on hiring only the best engineering talent, know that it's not that these people aren't smart, it's that they do not care.
It seems likely that Google incentivizes it's engineers not to care. The engineers get the crazy salaries and all the perks, they don't get to decide things. If you want to decide things, get promoted into product. You don't want to do product? You actually enjoy writing code? Then don't complain when your opinions and concerns are deferred. You could have switched to the business side, made less money, and hated your job.
Google used to be an amazing engineering company because it promoted an atmosphere where engineers wanted to care about what they were doing. They have been unable to sustain that dynamic as they tried to make the company good at things that were not engineering, and as a result, the engineers just don't care enough to save it anymore and you can feel it every time you use a Google product.