As the title says, would be great to move the synchronization process to headers-first sync.
It will definitely decrease the network latency in a big manner, the amount of data that needs to be downloaded and therefore the wallet initial sync.

This has been partially developed in the past inside our code, it requires further efforts to finish the functionality.

The only problem here and what needs to be described really well in a proper document is the PoS blocks validation and DoS spam protection.

We already added a sync spam filter when the "fake stake" attack was proposed. The topic, once headers-first is mostly done, will mostly be if this protection is enough or if there is a need for something different for PoS.