So it's the usual: make it available unrestricted on launch so that idiots build on your platform, look how many apps/extension we have. Once the market is captured, sorry is closed now, for we must protect our users.
Even if that's how it ended up, I doubt that was the plan. I think a lot of Google products, especially those from 10+ years ago, start out built for people like themselves: highly tech literate software engineers. As long as that is true enough, extensions are great and useful, and the users are mostly skeptical/aware enough to avoid installing malware. Now the average chrome user is the same person that filled their IE browser window with banzai buddy toolbars.
It never is the plan, I would say. Great products like chrome are made by people that are driven by the idea of making a great product, for the user. But after that is proven, given some time, the shareholders take over and priorities shift.
It also doesn't help that dodgy folks started buying trusted extensions. One update of a trusted extension and you're just as bad off as installing a dodgy one in the first place.