Are turret terminals robust for wire to boards connections as shown below? Are there other/better ways to implement this? It might depend on the application I think. I've seen these types of connections used for transmitting power instead of signals.
No this is a bad idea. Two problems come to mind immediately. One of the first things I was taught about soldered connections is that you should not rely on the strength of the solder to hold it together, that connection is doing that. In addition soldering the wire creates a stiff area which can result in fatigue failures of the wire depending on the operating environment.
I much prefer to use screw down or lever locked pcb wire connectors like the following.
Depending on your needs in a production environment you might want to consider a combination of cable connector and a compatible PCB header.