A-321 air carrier pilot reported a loss of hydraulic quantity during cruise. The flight diverted safely and was towed off the taxiway to the gate.

Narrative

We received a HYD Y LOW LVL ecam in cruise flight. Complied with QRH procedures; which resulted in Y system being unpowered. List of failures included Nose Wheel Steering (NWS). I contacted Dispatch and discussed options. I also consulted with Maintenance Conctrol to get their perspective on the failure and to ensure they weren't seeing additional problems on their telemetry. Considering our position and the fact that NWS would be inop; I decided that ZZZ would be the best place for a divert. I wasn't interested in continuing to ZZZ1; due to the loss of Nws and uncertainty as to whether I could clear the runway after landing. I also didn't want to continue into poor weather and risk additional failures to complicate the situation. Once the divert decision was made; we ran all the landing data calculations and informed ATC that we would like to divert to ZZZ and would need the longest runway. ATC said we would need to [request priority handling] to get the long runway; so we did. We also requested emergency equipment and a tug to tow us to the gate. I informed flight attendants and passengers of the situation and we continued for a normal landing in ZZZ. After clearing the runway onto a high speed; it became apparent that the plane would not make sharp turns with NWS inop. I stopped on taxiway; fire/rescue inspected us for leaks; and we got hooked up and towed to the gate.Cause: System failure. Hyd Y system lost all fluid.Suggestions: I don't think there is any way to prevent these kind of mechanical failures. Best we can do is be careful with procedures; ensure they are complied with correctly; and establish good communications as a crew to ensure nothing is missed. Also; take your time. No sense in rushing through any ecam. The only other suggestion I have would be to return to the old informal policy of no more flights after any priority situation. We used to always get removed from the rest of the flying during a day when anything like this happened. Scheduling and duty pilot seemed confused as to why I wasn't going to fly the next leg to ZZZ1. After any emergency divert; you simply should not fly any more legs that day. We used to have segments of our human factors class that highlighted the importance of taking time to recenter yourself and decompress after any such event. Any diversion with priority situation is a very high workload event; and you will find yourself distracted for some time after it. I would suggest that we establish a formal policy to remove pilots from any more flying after any emergency diversion. There have been incidents; Human factors class used to make it clear that continued flying after such an event is a bad idea. Huge distraction