Actually, the real answer is because your muscles fuse into one band of muscles further up the arm.
The fingers flex from muscle bands that contract, but they actually connect to your fingertips with tendons, and these tendons actually start before your wrist, so that only the tendons and very small amounts of muscles pass through the retinaculum and carpel tunnel in the wrist.
As you go further up towards the elbow, you will find that the muscle bands will fuse together since there isn't enough space for them to exist in separate bands. The nervous innervation is separate because you can flex them separately, however, since the bands of muscles are fused, flexing one of them partially flexes the other.
There are 6 muscles that flex the fingers.
But only two of them specifically flex the 4 fingers, and one of them flexes the thumb. The last three actually assist in flexing the whole hand and not fingers.
Flexor digitorum profundus and flexor digitorum superficialis.