Why does a phone maker get into banking transactions? Why does a social network build a virtual-reality headset? Why does an online retailer buy a grocery chain?

Amazon . com Inc.’s just-announced $13.7 billion bid to acquire Whole Foods Market Inc. is just the most extreme example of a larger, more consequential phenomenon: America’s biggest tech companies are spreading their tentacles, pushing into complementary businesses in a play to sustain growth as they saturate the market for their existing goods. Led by hard-charging executives, these companies are fueled by classic ambition—combined with the almost messianic attitude of those in Silicon Valley that tech can fix every industry on Earth.

The impact of all this is clear: Existing businesses that can’t respond by becoming tech companies themselves are going to get bought or bulldozed, and power and wealth will be concentrated in the hands of a few companies in a way not seen since the Gilded Age. The rest of us will have to decide how comfortable we are buying all our goods and services from the members of an oligopoly.

Think about it: Apple Inc., a computer company that became a phone company, is now working on self-driving cars, original TV programming and augmented reality, while pushing into payments territory previously controlled by banks, moves that could make it the first trillion-dollar company in the world.

Facebook Inc. , still seen by some as a baby-pictures-and-birthday-reminders company, is creating drones, virtual-reality hardware, original TV shows, even telepathic brain-computer interfaces.