PAR isn't any kind of panacea or golden rule for nodes in a distributed system, it describes properties of nodes that meet very narrowly-defined requirements, which are in no way universal, and which are in no way requirements for those nodes to participate in the distributed system.
More broadly, there's no concept of "crash recovery" at the system level, which has any meaningful utility. Nodes are either there or they're not there, exactly how they crash or recover from their crashes are irrelevant to the overall distributed system, insofar as if a crashed-and-recovered node comes back online, it's gonna need to re-sync with its peers before it can talk to anyone else, and that's not anything to do with "crash recovery" related to local disk or anything like that (which is all implementation details of the node itself) -- it's just normal node synchronization, orthogonal to any state storage stuff of the node.
PAR is something that your system can maybe implement, it's not any kind of rule or definition or requirement that all systems of some classification must satisfy..!
If I might add on to what you and Joran are both saying, after some time working with TigerBeetle, I found it useful to think of Protocol-Aware Recovery as similar to TAPIR (https://syslab.cs.washington.edu/papers/tapir-tr14.pdf). Normally we build distributed systems on top of clean abstraction layers, like "Nodes are pure state machines that do not corrupt or forget state", or "the transaction protocol assumes each key is backed by a sequentially-consistent system like a Paxos state machine". TAPIR and PAR show a path for building a more efficient, or more capable, system, by breaking the boundaries between those layers and coupling them together.
More broadly, there's no concept of "crash recovery" at the system level, which has any meaningful utility. Nodes are either there or they're not there, exactly how they crash or recover from their crashes are irrelevant to the overall distributed system, insofar as if a crashed-and-recovered node comes back online, it's gonna need to re-sync with its peers before it can talk to anyone else, and that's not anything to do with "crash recovery" related to local disk or anything like that (which is all implementation details of the node itself) -- it's just normal node synchronization, orthogonal to any state storage stuff of the node.
PAR is something that your system can maybe implement, it's not any kind of rule or definition or requirement that all systems of some classification must satisfy..!