What is Blitzcrank's main goal when he is not just playing hook casino?

Blitzcrank's most reliable build is the one that keeps his hook threatening while still leaving enough room to survive the answer. If a good catch too often ends with his own death, the build is not at the right level yet.

Why is mobility so essential on Blitzcrank even in a tankier version?

Mobility is essential because Blitzcrank loses a lot of value if he can no longer show a credible angle. As soon as the game closes his natural access routes, you need to help him recover a real catch threat.

When should Blitzcrank's build really be slowed down instead of simply pushing catch aggression?

When the lobby prevents repeated hook threat and surviving first contact matters more than snowballing the next pick.

Blitzcrank Wild Rift Best Build Guide (Patch 7.2a)

Blitzcrank creates value by forcing enemy mistakes. His build must maximize hook opportunities while allowing him to survive the critical moment of entering the enemy team to convert the hook into a kill.