Gary Illyes from Google responded to a Stack Overflow thread on the topic of rich snippets. He said, "No, review rich snippets should only be used in cases where "the main topic of the page needs to be about a specific product or service" -- using them on your homepage in general wouldn't be like that."
This is not new, but when I covered it when John Mueller said it back September 2014, some SEOs got angry.
The interesting thing is that Gary and John reference this guidelines document and quote "the main topic of the page needs to be about a specific product or service." But that language has changed a bit, now it reads:
Make sure the review or ratings markup refers clearly to a specific product or service as shown in the examples above. Do this by nesting the review or ratings within the markup of another schema.org type — such as schema.org/Book or schema.org/LocalBusiness — or by using that schema.org typed element as a value for the itemReviewed property.
It still does say "refers clearly to a specific product or service," but it has changed slightly.
Either way, 99% of the time, rich snippets do not belong on your home page. I know this will upset many SEOs because they add them to every page. But the more and more Google has to repeat it, you wonder when Google will start ignoring all home page rich snippets and/or issue manual actions for it.
Forum discussion at Stack Overflow.