Evaluate ongoing value of flatten-plugin-check #13965

The check was failing during the most recent release cycle due to dependency version bumps. We should evaluate if we should continue to run/maintain this check or if there's a way to make it less toilsome.

Context from #13938:

blakeli0: I think we should evaluate if this check still provides value. IIRC, there was a bug in the flatten plugin, so it was created to test the flatten plugin. But we should not test our build dependencies, the same as that we don't test other Maven plugins such as maven deploy or formatter.