ProxySQL in PXC and failing all nodes
No, installing ProxySQL is not mandatory 
Do you mean all three nodes close down suddenly rather than close down gracefully? What version of Percona XtraDB Cluster are you using? If it is a version 5.6.19 or later, then the nodes will read the last state on startup and will try to restore primary component once all the members again start to see each other. This makes the PXC cluster to automatically recover from being powered down without any manual intervention. This information came from https://www.percona.com/blog/2014/09/01/galera-replication-how-to-recover-a-pxc-cluster/ and you may find other useful blogs around this subject and/or webinars on the Percona site. 


Disclosure: I am from Percona