I think you're wrong, Chrono Cross was entirely based on Chrono Trigger, but only if you really understood it, you can see what they have in common.
Here are some similarities of
CC (Chrono Cross) with
CT (Chrono Trigger). May contain
spoilers, don't read if you didn't play CC yet.
First, if the Square would make a direct sequel of it, then it will be less original. Second, the story was entirely based on Chrono Trigger, it begins when Balthazar, the guru that appears on the first game, with his knowledge of the future, built Chronopolis and it was sent to the earlier past, the prehistorical ages and the computer Fate made El Nido.
Dinopolis the city of reptiles (remember Azala?), exists there.
Lavos fell and its radiation made the apes evolved into humans, then the war between humans and apes began, just like in the first game, and Chronopolis fought in the human's side. The reptiles ultimate machine the Dragon was divided into six weak creatures by Fate and scattered in different islands.
Serge is silent, like Crono, there are no random battles, like in the first game.
There are Double and Triple Techs, although the battle system changed, to be less FF related, I think.
The sword Masamune and those creatures that dwells it: Masa, Mune and Doreen appear too.
Glenn, is the name of Frog in CT, he appears in CC with green hair, with similar personality and fighting style, and also have X Strike Double Tech with Serge, just like Frog had with Crono.
Crono, Marle and Lucca all appear on CC as kids. Also Lucca is important on the story, she made an orphanage and raised Kid, the protagonist and also the Schala's alter ego, that princess of CT.
Serge saves Kid on Lucca's house on CC, it's identical to that one of CT, remember?
The Epoch ship appears on the basement of the library of Viper's Manor. That blue creature Squirt is like the Nu on CT.
Pierre has the Hero Medal and the Slice of Cyrus Tech, if you played CT, you know what I'm talking about.
Cats appear with abundance too, like in CT (*LOL*).
Lavos is the final boss, Schala appears with it and CC has many finals and the way it works is identical to CT.
There are some BGMs of CT on CC with new arrangements.
There's much more to say, but I think it's enough, after that if you say it has nothing to do with Chrono Trigger is because you didn't play or understand it or just because you're dumb
! Sorry if I took so much
space...