I don’t think that creative destruction and disruption only apply to Silicon Valley ideology (BTW I know and share your point of view on this topic), it’s a general process within business.
My point is that if you want to change something more radical about your business or move into a new area of business, you should do it outside of your current business. The benefits of this are that you don’t disturb your current business (and the way you make money) and you can limit the risk in case of failure (only the new venture would fail but not your core business). Let’s also not forget that there is a high probability that your efforts will fail and this probability will be even higher if you want to do something new within an old structure and system that is not designed to explore something new but to increase productivity.
How and if you need to integrate this new business in your current business is another discussion. Looking at the complexity of large cooperation, I would see a lot of benefits in keeping it separate unless there are strong benefits of integration and/or scale.