I think it would at least create a lot of hostility between Google/Apple, the developer ecosystem and the analytics industry. Third party analytics companies could have their lunch eaten entirely because Google/Apple have greater resources than them and would know how to obviate them using their own infrastructure. I could see very expensive lawsuits being brought against Google/Apple for doing this, or increased pressure for third party app stores or nontraditional app distribution channels.

In the short term you're probably right, nothing would "burn" except a lot of developer good will. But in the long term it'd be a great way to get many different parties thinking hard about how to get off your platform or replace you.