For such a model to work I believe you need a distributed replicated state machine, and the clients to be an active part of the distributed system (not just participating doing requests), being able to reply to pings. Yes, there is a safety advantage in the model you describe, as if the time taken to finish with an operation is larger than expected, the other clients may want to wait more, but in the practice:
1) What you do if the client replies to pings but takes an apparently never ending time to perform the operation on the shared resource?
2) What about if the client is correctly operating on the shared resource but the only component which is failing is the system you use to check its availability?