When is the floating IP or anything used?

Floats are used by virtual servers to talk to pool members (nodes). It is useful when you have have long running connections, so the mirrored sessions can persist after a failover. Otherwise, if you had to change IP addresses, session mirroring would be useless.

Another situation is when you use BIG-IP as a network gateway, so you can have only one destination in you routing table being served by any active device in your cluster.

Virtual addresses are always floating.

Monitors use local Self IPs. Some management tasks can use local SelF IPs or the management port depending on your configuration.