In my experience, applications and syntax come and go, but the data live on. Mortgages last up to 30 years, life insurance policies even longer. Databases can last much, much longer. Yes, this is a pain in the neck - but not the biggest one. This last part is perhaps the most important as the first two are trivial.
Network databases add direct entity set relationships and navigation to the mix.
No such base set of operations exists for object databases. Object databases provide great behavioral flexibility, but you give up some of the power of the standard operations. It is a data model for building data models. But I'm not sure what this buys you. I certainly don't see how you build a potentially large database of abstract nodes and properties and query and update it.