This is currently the weakest link in the overall Apple experience, and it gets even worse if you want to use, say, Google Contacts and Calendar.
Trivially so, since you said “no interest.” If they had none at all, why would they go so far as to actively support non-Apple services?
Relatedly, their aggressive support of the Web as a platform is by definition interoperable. Their best-in-class mobile browser (or nearly — source: PPK/Quirksmode) can almost be considered a universal interoperability module.