When is it a good idea to use something like CRDT instead of paxos or raft?
If you can use something like CRDT, do so. You should get much better performance. It also enables interesting use cases such as working offline and then merging later. However it is not always possible to design things such that a CRDT will work for you. In that case, paxos can solve the hard problems for you.
But even if you've decided to use paxos, generally you should limit how much work is being done directly through the paxos algorithm. Instead for performance reasons you want to reserve paxos for necessary operations such as master election, and then let a replicated master setup handle most decisions. (In a high throughput environment the master is likely to do something like delegate responsibility for specific shards to specific children, which replicate off each other. Do not let the master become a bottleneck...)
That said, it is much easier to claim that you'll wave the magic wand of paxos than it is to actually do it in practice. In that light you may find http://static.googleusercontent.com/external_content/untrusted_dlcp/research.google.com/en/us/archive/chubby-osdi06.pdf to be an interesting description of the difficulties that a real-world paxos implementation is likely to encounter.