The Feature
As of SQL Server 2012, using local disks for TEMPDB on a failover cluster is a fully supported feature. In the light of fast storage solutions (SSD / NVME) directly plugged into the mainboard of a system, this is a big step forward because before that there was no way of providing storage to cluster (SAN) storage that is anywhere near as fast as local storage.
The Problem
There is a caveat: that local disk turns into a non-clustered resource on which your SQL installation depends and the cluster service has no way of knowing the health state