Those companies will die...
Their business processes and products are often sclerotic, and so are vulnerable to disruption by smaller, more nimble startups. That's the central premise of virtually all B2B software from the Valley. But they certainly aren't going to die.
In fact, large companies and enormous capital are required to take things from a "disruptive innovation" to a household name, to say nothing of providing an exit for SV startups. So, they're a vital part of the biosphere and they're not going anywhere.
I think this is becoming less and less true, unless one is competing with the tech giants directly. In the past enormous capital investment was required to build out the minimum viable capacity needed to serve larger customers or market segments. Today you can rent that capacity. In the future more and more types of capacity can become rentable, such as logistics, compliance, manufacturing, etc.
Agile is not always the right approach. For highly regulated or safety critical industries, it's quite likely to be the wrong approach.
(On the other hand, Waterfall for B2C mobile apps or casual games is also almost always the wrong approach too...)