Spoken like someone who has not tried what you are describing. There are two moving parts to your response: a locally
hosted runner awaits jobs from GitLab itself, which doesn't help running _locally_, and the other part is that -- back when it existed! -- trying $(gitlab-runner exec) was not a full fledged implementation of the GitLab CI concepts, making it the uncanny valley of "run something locally."
However, as of v16 there is no more exec https://gitlab.com/gitlab-org/gitlab/-/issues/385235 which I guess is good and bad. Good in that it not longer sets improper expectations that it could have plausibly done anything, and bad in that now it joins GitHub Actions[1] in not having any _local_ test strategy aside from "boot up gitlab/gitlab-ce && echo good luck"
1: yes, I'm acutely aware of the 3(?) implementations/forks of nektos/act that claim to do GHA but, again, readme is not software and I can tell you with the utmost certainty they do not do as advertised