I use dshackle to load balance incoming RPC requests for ETH1. Recently, I tried to look for the same solution on ETH2/beacon-chain, and I found an old repo that service doesn't work correctly when I deploy it.
It's possible to do so using general web load balancers like Nginx or HAProxy, but we have to use a single client (lighthouse, prysm, etc) due to different implementations of beacon-chain clients.
PS: Round-robin DNS is not that intelligent and useful.