There is a certain mechanical elegance in keeping point defense focused purely on countering missiles, but if you want to open up for consideration broadening its functionality, there is significant precedent in both science fiction and the real world for allowing PD weapons to target fighters.
For science fiction, I was actually surprised to find that PD weapons couldn’t target fighters because I’m used to space combat games treating point defense as a general anti-fighter and anti-missile package. This simplifies the rock-paper scissors somewhat by letting you build more generalized defenses for your ships. If PD weapons have sufficiently high tracking and low damage and penetration, this could give armored bombers a real role, assuming that they are boosted to be better able to evade anti-ship weapons.
For the real world, anti-fighter and anti-missile point defense are nearly identical technologies that involve equal amounts of firepower and targeting finesse, as they are both variants of “shoot down a small, fast, and very dangerous object in the sky”. The US Navy uses a multi-tiered system that includes missiles and computer-controlled Vulcan cannons as their anti-missile point defense. The multi-purpose SAM missiles that the US Navy uses to intercept anti-ship missiles are also designed to target incoming fighters as needed. The Vulcan cannons, while primarily purposed only as a very short-range last-ditch anti-missile system, nevertheless are the same gun that serves as the standard air-to-air machine gun mounted on F-14s, F-15s, F-16s, F/A-18s, and F-22s, and have accident-proven ability to take out combat fighters if such circumstances arose that it would be necessary to co-opt the gun in that fashion.