Why would you use Function instead of the already existing Consumer or Supplier?

Because we need to change all the interface, this is an issue that it's going to be integrated in a major release. I don't know right now when that it's going to happen.
I don't think you need to add additional JIRA for this issue.

> More “conservative” solution could be to annotate existing interfaces with java,lang.FunctionalInterface annotation and use them as it’s now.

As far as I can tell there is no difference between the already existing interfaces and the one in java.util.* I prefer to use the one in java.util than re-invent the wheel. It's possible that while working on the issue we notice something different and change idea.