I think our points of view are actually very strongly aligned. However I believe the next big idea is likely to come from outside of computer science.
Personally, I am betting on biology. So many of the most sophisticated techniques are based on biology, e.g. neural nets and genetic algorithms. I have done a lot of work on extending the theory of computation with a new axiom which gives Turing machines a self replicating axiom[1], [2]
In many parts of science, there is a cross pollination, where new ways of thinking about subject X come from a new discovery in subject Y. Typically, research will follow a group think pattern until it hits a brick wall, then you need that really big breakthrough idea. This line of reasoning leads to the conclusion, imo, that it's approximately equally likely to come from either pure computer science, or pure mathematics, or somewhere else.
[1] https://math.stackexchange.com/questions/3605352/what-is-the...
[2] https://medium.com/swlh/self-replicating-computer-programs-8...