Inter-VRF Route Leaking

We currently have a topology in our data center network where each ISP is in a different VRF. We added a P2Pcircuit to another data center and want to route site to site traffic each site’s public IPs via the private link. In order to do this, the routes in the VRF need to be leaked to the private routing routing table, and the IPs announced from the private routing table need to be leaked into the ISP VRFs. We wanted to use BGP and not static routes, in case there was an outage on the private link, then traffic would again route via the Internet

So, from a design clinic perspective, I would like to see when leaking makes sense, why you would or would not use route leaking, and what are the pitfalls.