You can also keep persistent connections with HTTP to avoid the overhead, which is what Tinybird does. (I used to work there)
https://clickhouse.com/docs/concepts/features/interfaces/htt...
If you throw something like nginx in front to try to better guarantee the "balance" part of load balancing, as an improvement over TCP connections that are sticky to the initial server they reach, then you're asking different CH servers to handle the same original session. So what did the load balancer give you?
Now, CH added session-aware routing for the HTTP client... but it's a beta feature, and it requires an Enterprise license anyway: https://clickhouse.com/docs/products/cloud/features/infrastr...
Why go against the tide?