Webassembly is relatively new, but expect many websites to start implementing newer client front-ends in wasm as opposed to JS in the nearish future, at least partially. Disabling it would only make sense if you also intend to disable JS, which is your choice but just makes your life harder =P
* I'm aware it's incorrect. It's just an illustrative example.
Some highly technical users will have some idea of what the implications of each answer are, but for them you are better to use the proper name ("WebAssembly"), since then it will be much clearer what the question actually is asking about.
[1]: Chrome stopped asking and won’t run Flash until they click though a couple menus to enable it.
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Edit: I just remembered that WebAssembly has JavaScript based polyfills. Disabling WebAssembly does not do me much good, as it will still run. No dialog can really stop that...
In order for a permission prompt to be meaningful, the tradeoff must be immediately obvious. For instance, "Allow this website/app to use your camera?" is a meaningful prompt. You might want it to use features involving taking photos; you might not want the site or app to see where you are.
But what is the downside of high-performance computing? And how am I supposed to meaningfully evaluate (even as a security nerd!) "Allow high performance computing that might steal secrets from your machine?" Why would I ever say yes to that?
Not everyone is on a battery-powered device, and also, it's often true that "high performance" means "it completes faster and therefore spends less energy." Certainly if saying no often triggers a polyfill in actual web apps, people will quickly learn that high performance means less battery.
Agree about news pages but I wish we'd prevent them from using any serious amount of CPU, whether in wasm or JS.