A customer asked this question to support recently. I thought it could help the community with clearing up this possible misunderstanding as it is not really mentioned in the documentation:
"In a distributed server environment, is it required to install a JWP on each node where the AE is installed?"
The answer here is no. It's not required, but it is recommended to include a JWP on each node so you can use the benefits of the JWP should your primary node go down.