For most WebGL errors/messages, if there are "too many", they will no longer be printed to the console.
This doesn't seem to be true of the non-blocking readback performance warnings I added recently ( issue 828135 ):
https://cs.chromium.org/chromium/src/gpu/command_buffer/client/gles2_implementation.cc?l=5211&rcl=e13e548536440ee7c9104ccaa0f6190438a01605
https://cs.chromium.org/chromium/src/gpu/command_buffer/client/gles2_implementation.cc?l=5775&rcl=e13e548536440ee7c9104ccaa0f6190438a01605

But they should be limited by the same mechanism (WebGLRenderingContextBase::PrintWarningToConsole does this).

I'm not sure how gles2_cmd_decoder's performance warnings are wired up, or whether they are also limited, but they might help find the way to implement this.
https://cs.chromium.org/chromium/src/gpu/command_buffer/service/gles2_cmd_decoder.cc?l=234&rcl=ffeff6a71e41c4088e8f8b898ab381c54a41ef02