I think the issue you're looking for is a limited number of supported datatypes. This doesn't appear to be a general-purpose database at the moment: don't expect to drop it in as a replacement for MySQL. Doesn't mean it can't be in the future, but it would have to fall back on other techniques for the datatypes that can't be built with CRDTs.
I think the data types look fine. If I'm using such a database, I don't think I want the CRDT data types to be abstracted away behind some general-purpose (SQL?) interface. Can that even be done? I'd rather just pay the small price of restructuring my data into maps and sets and have the CRDT database do the rest without any extra indirection.
Well, i've been working on an SQL interface for AntidoteDB for my master thesis, and yes, it can be done. However, there are some limitations. At this point we are mostly focusing in constraints (i.e. invariant preservation), and we've already figured out stuff like numeric bounds, entity integrity and referential integrity (this last one is quite interesting IMO).
Github: https://github.com/JPDSousa/AQL
http://syncfree.github.io/antidote/crdts.html