It seems somewhat unnecessary since Elasticsearch already has distributed features built in. For instance, it natively scales out across multiple nodes, replicates its data, and automatically recovers from partial failures.
Remote storage also tends to have much higher latency than local disks, and this can have a big effect on performance.
Elasticsearch presents a particularly stressful workload to the filesystem and turns out to be rather good at hitting filesystem bugs and corner cases that other tests might have missed. This is true even of very mature and well-established filesystems. Distributed filesystems have seen much less production use and therefore seem a much riskier choice. See for instance this post with some links to recent glusterfs bugs: