Prediction: someone deploys this and doesn't notice it's incredibly slow for mysterious reasons, and then spends several hours to figure out that the right version of CUDA wasn't installed. ("Fail fast, fail loudly" is a nice way to ensure that doesn't happen.)
I've never done front end development but I would probably want to request permission to gather telemetry, and, if granted, post the telemetry and the error to an error logging service. Then you could try to diagnose aggregated issues. You could also offer the option to export the telemetry to a zip file (hopefully the same format you send it to the error logger). Then the user could examine it themselves and have the option to provide it to you via another channel (support forum, email, etc.).
Do the opinions of potential users matter? Because most people aren't willing to waste money on unnecessary upgrades just because a developer wanted to assume everyone had mid/high-end hardware.
Why not just print out a message "Running in CPU mode" or "Running in GPU mode". There's no reason it has to be a mystery.
The comments here tell me that programmers have a narrow idea of what other programmers should/would/could do with their software.
Fix their GPU drivers or OSes. In a cloud, switch to GPU instance type.
Compute shaders were introduced in Direct3D 11.0, on PCs the support for them is required for a decade now. Mobile devices were a bit later, but their upgrade cycles are faster, the support is good by now.