in which scenario is a full proxy TCP connection required?

DNS load balancing resolves client queries to a server IP address directly, so the client connects to the server without any intermediary TCP proxy being required.

Source NAT rewrites source IP addresses and can be applied in a pass-through or one-arm mode without establishing a separate proxy TCP session toward the server.

Preserving the original client source IP on the server side is actually easier in a non-full-proxy pass-through mode; full proxy by default replaces the source IP and requires extra configuration such as X-Forwarded-For to convey the client address.

In a full proxy model the BIG-IP (or any full proxy device) maintains two completely independent TCP state machines - one facing the client and one facing the server - with the proxy mediating between them. This decoupling is the defining architectural characteristic of a full proxy and enables the device to buffer, transform, or optimize each side of the connection independently regardless of what the other side is doing.