This question somewhat relates to Another question but the other way around.
We use one domain with hostnames that resolve to public and hostnames that relsolve to private IPs. I agree to the answer to the aforementioned question that I don't see this as a security thread. Especially relative to the afford of configuring and running an Split-Brain-DNS for this important domain.
Therefore we decided that we will not host internal DNS Servers and therefore won't have reverse DNS for internal IPs. Now I found out that I can register the domain '10.in-addr.arpa' with our DNS provider. So I could in theory host my reverse DNS zone there. I could configure the local caching DNS Servers on all sites to lookup requests for 10.in-addr.arpa on that server and would have reverse DNS working + the API and interface of our DNS provider.
On the other side that is a public DNS server. So everyone asking it for e.g. 126.96.36.199.in-addr.arpa would get our local hostname as response.
Do you think this is a bad idea aside from the aforementioned information leakage that we are willing to accept.