Why DNSSEC and Secondary DNS may not work together
All authoritative name servers MUST sign all record sets with all private keys that are Zone Signing Key (ZSK) type. This is necessary because a resolver could get the ZSK from one authoritative name server and the RRSIG from another authoritative name server. To include the RRSIG for all ZSK DNSKEYs, the authoritative name servers must have all private key material. We currently do not share private key material, and even if we did, AXFR does not support transferring private key material and thus key rotations would have to be done manually in a coordinated fashion.
Note that in practice, it is possible to run multi-provider DNSSEC without sharing ZSK private key material, however it is not guaranteed to work due to the condition described above with resolvers getting the DNSKEY and the RRset + RRSIG from different authoritative name servers.
You can read more information about multi-provider DNSSEC in this Draft RFC here.