Well-maintained planes don't do that.
Take-off asks a lot from the engines, and one nasty bit about manufacturing defects is that they can take a while to show up, but the bulk of them usually surfaces when the aircraft are relatively new.
But: this plane was delayed before the flight due to maintenance on engine #1, so that's the first place where I would start looking for issues without any kind of judgment beforehand on what you would expect to find. And that's the main issue with that comment, it assumes a conclusion, that's not how these investigations work because then you might miss the actual cause. And given how critical these machines are it doesn't take much. All it takes is a single, tiny mistake.
The really bad luck here is that it seems as though the failure of engine #1 took the center engine right along with it. That's one of the issues with that particular design, if you have debris from one of the forward engines it could easily get ingested by the rear mounted one.
https://en.wikipedia.org/wiki/US_Airways_Flight_1549
Once an engine breaks the question is whether or not it becomes unbalanced, that is one reason why they can become detached from the plane.
> In an effort to prevent similar accidents, officials captured and exterminated 1,235 Canada geese at 17 locations across New York City in mid-2009 and coated 1,739 goose eggs with oil to smother the developing goslings.[71] As of 2017, 70,000 birds had been intentionally killed in New York City through programs instituted after the ditching.[72]