Thankyou, that's a good point about performance. The goal is for preventing blocking. We're not trying to offload processing since we have Server1 Replicating to Server2 and Server2 replicating to Server1.
The reason for the Linked Server rather than connecting directly to the secondary is because a Stored Procedure could read from the secondary and later in the same Stored Procedure could write to the primary.
But I'm not disagreeing that there could be better ways to do this.