Ever try to start an adventure plot in motion by kidnapping or threatening an NPC the PCs are supposed to care about, only to find your players yawning? Put yourself in the player's position. "My brother was kidnapped? I have a brother?"
Most RPGs stress the adventure, not the downtime. Some players have elaborate backstories with plenty of NPCs for you to threaten, but most... not so much. How do you get the player to care about an NPC as much as their powerful weapon?
Make the NPC Useful to the Character
Got a sister in a fantasy game? She can make potions at half price. Not an infinite number, but a few a session. Your player will start appreciating her in a whole new light. They might even remember her name!
Got a carriage driver in a steampunk game? He can tell fortunes that give the player clues about what's coming next. When he talks about death walking in flames, it's time to find some fire protection.
How about a mother with contacts that give the player bonuses when dealing with the upper classes? An uncle with contacts in the underworld? Contacts that remind the PC why they are bothering to listen to them. "Always liked your mother." "No one could shiv a guard like your uncle..."
Or a seamstress/tailor whose clothes give a bonus to social rolls. But only for a season, then fashion changes.
Do this for a few sessions. Then kidnap the NPC. Or threaten them in some way. All of a sudden, your players will find they do care.