The reason the main heroes seem to have met with a shadowy fate (and I'm not enitely sure they did actually die) is because Chrono Cross is all about consequences.
In Chrono Trigger, the gang have a jolly romp through time, and it never seems to have anything but good consequences for them. Chrono dies, and with a bit of adventure, they manage to bring him back. Everything goes right, and it never crosses their minds to consider the implications of what they are doing. They're changing history!
Chrono Cross is the big plot twist of the series. Suddenly, after everything seeming all bright and wonderful in CT, you get slapped by this...And personally, I think you're supposed to feel it. The CT gang aren't kids any more. When they were young, running aound through time was all fun and adventure and to them they saved the world. Chrono Cross, you suddenly see the results from an adult perspective and go 'whoah...uh oh. They messed up time and space a bit, didn't they?'
I admit that CC wasn't as much FUN as CT. But it made me think a lot more. CC is a much more 'grown up' game that deals a lot with the complex nature of time and space and the consequences of actions. For this reason, had they used the Shounen Jumpy, bold drawing style of Toriyama, it would have looked wrong. CC may be bitter medicine, but you have to take it in order to experience and appreciate the Chrono series as a whole, by facing the consequences that were ignored by the naive youngsters of the first game and tying up all the lose ends.