Not a bad idea, but that only delays the necessity of a resync until the next failover…. Unless I’m missing something?
I've used cascading replication extensively over the past few years and rarely had to resync a downstream replica. The several thousand Postgres clusters I'm administering now are almost exclusively set up with the primary replica streaming from the master and the master shipping WALs to the secondary replica in DR data centre, so I can't test any cascading replication promotions at the moment. My suggestion is to test your replication setup in a cascade and see what happens, I don't expect you'll need to resync. If you do, report back with how you've set up your replication settings.