I am setting up an on-prem app to send data over to cloud. While evaluating the usage of a message broker, I read that there will be persistent connection between on-prem and cloud. Cloud is where the message broker queues are present.

1. If we are talking about a 1000 instances of these on-prem apps(from 1000 customers), what are the flaws/cons/issues of having so many persistent connections?
2. What can be done to tackle these issues?

Please note that we do not plan to use any cloud specific services(from aws etc.) for initial few phases.

Any other feedback is welcome too.