Nowadays, are large ships well protected from small unmanned underwater ships? Are they worth building?

The large ships are well-protected. A “small unmanned underwater ship” has been a primary threat model for a century e.g. heavy torpedoes. These already have very long range and sophisticated sensors that allow them to hunt targets autonomously.

The other side of this is that modern large military ships are almost literally unsinkable. It is very difficult to get enough explosive on target due to their extreme damage resistance.

When the military does live fire exercises where they attack obsolete military vessels with no active defenses using torpedos, missiles, bombs, etc, they usually don’t manage to sink it. They have to send a specialized demolition crew afterward to actually scuttle the damaged ship and turn it into an artificial reef.

An operational large military vessel will have layers of substantial active defenses that make this even more difficult.

Yes to being worth building.

The whole point of the navy is to be able to control waterways. The whole point of being able to control waterways is to be able to economically ship large amounts of material and people; in the case of warfare, soldiers, bullets, food, water, fuel, etc.

An unmanned fast attack sub is going to be useless for defending your logistics fleet from strike fighters and anti ship missles. Even a dingy that has a guy in it with a rocket propelled grenade can send a cargo ship to it's grave. You have to have a surface ships with powerful defenses to protect them.