Good question, still a "green" technology but I have had great successes with it for the past 4-5 years in production (ASM.JS before widespread WASM compatibility).
"promising that we'll be able to build web apps in any language" is not how I see WASM, nor is it really used in this way outside of transpiling Unity3D/Unreal games (this may be the one area there is an exception). I use it to transpile C++ to WASM libraries used within React apps, Edge Lambdas, and Node.JS servers. Primarily down to 2 reasons: speed and efficiency. WASM unlocks excellence and resources in other disciplines/languages such as AI and AR tool chains, Engineers, OpenCV, etc. When used like this, it is outstanding.
What WASM will never be good at is being used for the whole experience. You lose the semantic web, and/or accessibility tooling. Web has some outstanding guidelines and frameworks to help the impaired, screen readers and the like. Using WASM to pump a native app into a HTMLCanvasElement will lose all of these advances, therefore, WASM shouldn't be used for this use case (outside of games). Like all tooling, there is a time and a place to use them.
Below are a few links which use WASM in production:
https://holition.com/play/holition-brings-home-twenty-awards...
https://winners.webbyawards.com/2020/apps-mobile-and-voice/a...
https://www.youniqueproducts.com/beautyguide#.YIS9hOhKguU
https://www.charlottetilbury.com/us/products/charlottes-virt...
https://visagetechnologies.com/demo/
"promising that we'll be able to build web apps in any language" is not how I see WASM, nor is it really used in this way outside of transpiling Unity3D/Unreal games (this may be the one area there is an exception). I use it to transpile C++ to WASM libraries used within React apps, Edge Lambdas, and Node.JS servers. Primarily down to 2 reasons: speed and efficiency. WASM unlocks excellence and resources in other disciplines/languages such as AI and AR tool chains, Engineers, OpenCV, etc. When used like this, it is outstanding.
What WASM will never be good at is being used for the whole experience. You lose the semantic web, and/or accessibility tooling. Web has some outstanding guidelines and frameworks to help the impaired, screen readers and the like. Using WASM to pump a native app into a HTMLCanvasElement will lose all of these advances, therefore, WASM shouldn't be used for this use case (outside of games). Like all tooling, there is a time and a place to use them.
Below are a few links which use WASM in production:
https://holition.com/play/holition-brings-home-twenty-awards...
https://winners.webbyawards.com/2020/apps-mobile-and-voice/a...
https://www.youniqueproducts.com/beautyguide#.YIS9hOhKguU
https://www.charlottetilbury.com/us/products/charlottes-virt...
https://visagetechnologies.com/demo/