Hi Piotr,
the primary reasons for sending GARP are to update the peripheral switches L2 forwarding tables (aka CAM tables) and to update the ARP cache of routers / firewalls / servers in case of a failover.
The unit becoming active will send GARPs (as you already traced).
This way it should not be necessary to clear ARP caches of peripheral devices manually. Due to the long ARP cache lifetime on these devices, services provided by the BIG-IP may seem to be unavailable until the router / firewall / server updates it´s ARP cache due to timeout.
Thanks, Stephan