Instead of using short range celestial bronze (CB) weapons like swords and arrows why not make advanced weapons like machine guns or grenades with CB shrapnel in it?
Frederick Chase, Annabeth's father had created bullets with celestial bronze casings.
Her father blushed. "Well, not bad for a middle-aged mortal, I suppose." "But the celestial bronze bullets! How did you get those?"
"Ah, well. You did leave quite a few half-blood weapons in your room in Virginia, the last time you... left."
Annabeth looked down, embarrassed. I noticed Dr. Chase was very careful not to say ran away. "I decided to try melting some down to make bullet casings," he continued. "Just a little experiment."
Percy Jackson and the Olympians 03 - Titans Curse, Chapter 18, A Friend Says Good-Bye
Celestial Bronze is not a rare element according to wiki
Celestial Bronze is normally mined from Olympus, if Hephaestus is upset with his work, he throws pieces of Celestial Bronze into the mortal world.
Celestial Bronze seems almost as abundant as iron to Greek Demigods, as not only their weapons made out of it, but it seems like almost everything the Greek Demigods make is made out of it, using it as a magical alternative to what other metals would normally be used for weapons. Though this is justified as its mined from Olympus which is right above the Empire State Building.
I can think of few reasons why modern weapons are not used regularly
The quest our heroes take are of longer duration. Modern weapons like guns would run out of bullets and heroes cannot come back to Camp Half-Blood to get more ammunition.
Not all heroes are like Leo Valdez, who can create new weapons/machines whenever required.
Traditional weapons don't need to be recharged and they add more drama, because heroes would have to get close enough to the monsters to kill them.