So the gods are more powerful as more people believe in them, right? And if people stop believing in them their power fades. What if the same is true for the demigods?
Like Percy got stronger because he got older, yes, but also because people believed he was capable of more destruction. The Romans fear Neptune, so they were afraid of him. That affected his powers somewhat negatively if I remember correctly. After he reunites with Tyson and Annabeth, people who believe in him, he gets stronger again.
The same with Nico. when he was younger he wasn't that strong with his powers at all. As he grew, people believed in his destructive abilities more and he got stronger.
Piper used her charmspeak to steal cars and stuff like that before she knew she was a demigod. I assume she had to practice to get better at it. We see in the books that she has people believing in her ability, and she is able to talk gods and monsters down.
I just think it would be interesting to see how much everyone's belief would affect the strength of the demigods and their powers. I also think their belief in themselves and what they are capable of helps as well.