The problem is that companies get really good at solving yesterday's problems. In Intel's case, that was making great CPUs for desktop PCs and servers. I have no doubt that the absolute pinnacle of desktop PC CPU engineering, was done at Intel in the last ~10 years.
The problem is, the world changes. Growth shifts from PC to mobile. People in datacenters start worrying more about cost and energy efficiency and build their own ARM parts. The landscape shifts, and the company is still fighting yesterday's battle. But it doesn't matter anymore-the basis of competition has shifted.
I think it's very difficult to pivot a company's core "basis of competition", or as you've elegantly put it, "self-image". What are we best at? Why are people getting promoted? Who's in leadership roles? The answers to these things need to shift over time, but most companies can't. This is why companies rise and fall.
I think a big problem with Google overall, is that their self-image isn't really customer-oriented. It's more inward-looking, "we're great engineers", "we're not evil", "we build the best distributed systems". The meta lesson is perhaps, orientation around serving your customers is the only thing you can fix, long-term. Amazon gets this. The problem is, it's way more nebulous and hard to pin down, than some of the more specific things Google has anchored on for the past years.