At the start of disc two when you start learning more about Lynx past, theres literally 1 line of dialog that says something like him destroying with ease the past keepers of the flame (Chrono and company) because he was using the new school magic as opposed to their old ineffective style.
Which is, apparently, why ~90% of the people that hate Chrono Cross hate it for.
Yeah, there was that. Hell, there is a part where you use either the Chrono Cross or Mastermune and visit Lucca's house while it's burning (which Lynx is responsible for). The only purpose it served though was re-adding Kid and getting her Level 7 tech.
Speaking of spells, the Element System in Cross has plenty of problems.
For starters, you could only use all your spells once. Unless you used Chrono Cross (which you didnt get until later in disc 2), and one character has a skill to do that (Leena). Which was a problem in many boss fights.
Second, the field effect could work for and against you. Like if the thing was entirely green, then green spells/attacks doubled and yellows (it's weakness) would virtually do no damage.
And third, a vast majority of characters except for the main, and a few you start with will have shit Magic anyways. Your main character is rigged in the end.
I personally liked the game, but there were a few things they could have improved on.