Often an exceptional condition is not a 4xx error code, it might be a redirect or require custom headers or content.
See https://gerrit.wikimedia.org/r/c/mediawiki/services/parsoid/+/621558 for the use case, where a redirect (with custom headers) is the exceptional condition caused by a failure to extract a page id.
I'm a bit dubious about the idea. While I can see that this would be useful in some cases, it should not be the rule to use exceptions to generate non-error response. it seems to me like in most cases, this would obscure the information flow.