Why is it easy for the people who has been in martial arts for a long time to mix training and be mma instead of being good at just one art / sport .

 

when you mix arts you realize they are all the same an armbar is an armbar and a hip throw is a hip throw . How you articulate the art is the difference and culture of the arts . 

Japanese Jujitsu and Nin Jitsu are the same art . 
one adds more weapons / swords / out door survival / making of weapons and Ninja training .

while the Jujitsu teaches the same art with all focus being on fighting and street survival with mma sport of well rounded standup , takedowns , and submission grappling with management in ring and time set sparring . 

Hapkido is the same has JuJitsu 100 % self defense with more kicks like Taekwondo. 

TaeKwonDo and Karate are similar.
In karate the continous karate sport is like kickboxing in a south paw stance , point sparring kicks are done with lead leg and back fist , back hand , reverse punch I use more ofthen .

Taekwondo is more continuous like kickboxing both legs coming at you but hands are in a chamber position snapping hips and upper torso in the punch like boxing . 

American Kickboxing is boxing add the kicks that come from karate and taekwondo - waist to head level . 

 

muaythai is American Kickboxing but add low chopping kicks to the legs with knee strikes and elbows with head butts . 

Brazilian Jiu Jitsu is submission wrestling- get the fight to the ground and submit an attacker or opponent with out throwing strikes . With takedowns that deliver you're opponent to the mat safely. 

while Japanese / Nin Jutsu/ Hapkido are mainly used for self defense they can be modified into sports combat arts 

 

Karate , TaeKwonDo, BJJ , boxing , American Kickboxing, Muay Thai are full contact combat sports