Episode 3, while certainly the best of the "new trilogy" was still mostly stupid.
Mario's story has always been absurd and stupid. What did you expect? Mario: Shakespeare? He's a plummer (most of the time) who saves a princess from a dinosaur.
Also, the Final Fantasy games mostly don't follow the same story, so that's a moot point.
Chrono Trigger had two sequels which weren't "entirely" sequels. If they make a new Chrono game, it won't effect anyone's (who isn't stupid) opinion of the previous Chrono games. A sequal does not tarnish the original. The original will always be there, just as it was...But as long as they get Kato, Mitsuda, & Toriyama, in my eyes, they can do no wrong to the series.