But sometimes SeriousCompany says "we'll provide this public resource so people can do X, Y, and Z", and then someone does A and gets a cease and desist?

It's an open resource, sure, but the provider of the resource can still set limits on its use, even after it's been available for some time. Often that includes things like "don't use our free resource to make yourself money".

That seems like an entirely reasonable request to me?

Something being freely available does not inherently grant you the right to use it however you'd like. It's pretty unhelpful to conflate the two things.