Personally, I believe it is inevitable that a vast and rich new mathematical world will spring up around simple computational systems, where they are the primary object of study and not relegated to being games, "simulations" of something else, curiosities, etc. CAs are just the "hello world" of this universe.
In that future, your attitude will be seen as a kind of parochial holdout of 20th century attitudes.
The new mathematics will:
* privilege finite, discrete systems
* be explicitly constructivist
* not shy away from computational enumeration and classification
* be much more visual, but no less rigorous than our last few hundred years of mathematics
* make deep connections with many new technological systems, like Git, distributed systems, blockchains, computer networks, trust networks, social networks, etc.
* most importantly, be way more fun than old math!
It will exploit to the full the capabilities of computer systems to make the new systems tangible, so that the idea of a 'math paper' will be itself quite old fashioned -- most mathematical work will start with forking a Git repo or the equivalent, and most communication and education will be interactive interrogation of computational systems using a kind of souped-up, computation-focused REPL. It's the kind of mathematics that will be natural when Brett Victor's ideas are actually implemented.
Wolfram's NKS book is the prototype work of this kind, but it will also be seen as quite a product of its time and of the author's prior commitments to physics, math, etc. And of course distorted by the classic Wolfram immodesty.r