The big brands are not unaware of this shift at all, but this isn't the usual tech story of one overarching monopoly being toppled by a disruptive newcomer that then becomes a monopoly (and repeat...) - the car business is far more diverse, and doesn't gravitate to one pole the way IT does.
If there's something you're not considering, I think it's how the average customer will treat autonomy. For personal transport, it's not a product category, but rather a feature. An important feature, but a feature nonetheless, and one that may not be too desirable outside of the unique traffic environment of the mass-transit-starved SF Bay. [ Freight and logistics is a completely different matter, but nobody in "tech" seems to care about goods transport, because they don't own vans ]
You drive a BMW. BMW does not make its own transmissions. It relies on specialist companies (Getrag and ZF-Friedrichshafen at present) to provide it with suitable systems. Similarly, everything in the interior of your car is made not by BMW, but by other companies: Adient (seats), Faurecia (dashboard trim), Magnetti Marelli (switchgear and instrumentation, and external lighting).
So, let's say BMW wants to make autonomous cars on one side, and Uber/Google/whoever wants to make autonomous cars on the other. Whereas the Silicon Valley people have to source and build everything around their big feature to make a car from it, the likes of BMW simply has to find one of the many autonomous-vehicle companies and strike a deal with them to build that killer feature into a BMW.
This is how the car business works. Most "innovative technologies" pioneered by car brands are from third-party suppliers who specialise in these things.
If it's "just mechanical engineering", why has Waymo/Google abandoned its grand plans to build autonomous cars, and partnered with Fiat-Chrysler instead? Google can get the userbase it wants without having to put pour to twenty billion dollars into developing a wide-range car manufacturing business, in an already fiercely competitive market with narrow margins and an unknown chance of success.