Creating fanwork is one thing. I've got no problem with that. Most of the time, a healthy fan following benefits the companies that produce the original material. (Just look at the Zelda or Star Wars franchises.)
But at the same time, I have no problem with a company defending its intellectual property. Not only are they within their legal rights to issue these C&D directives and bring further litigation if infringement continues, but it is in poor form for people to denigrate them for defending themselves in this fashion.
In other words, I believe we should respect the choices an intellectual property holder makes. It's their property, after all. They are rarely draconian in the exercise of their rights, as evidenced by the continuing prosperity of this very Compendium, which is full of copyrighted material that is republishered here in public without SE's permission. When they feel that a particular project threatens them--such as the creation of a fully functional Chrono game--and take action to eliminate these threats, I think it's proper to give the property owner the benefit of the doubt.
Few of us, if any, would be indifferent were we to create our own wildly successful intellectual property only to see creative control or profitability wrested from us at the hands of zealous fans.
As to the broader question of the validity and future of intellectual property rights, I think that we really ought to amend the laws to designate when property rights apply and when they do not. My basic, preliminary, hole-filled suggestion:
Property rights should apply when:
1. Creative control is at risk;
2. Profitability is at risk;
3. Long-term profit potential is at risk.
I think a large Chrono project violates the first and third of those. It changes the public's perception of the Chrono name and all that it entails. It adds to and changes the look and feel of the Chronoverse. It can change people's taste for the franchise and thus potentially turn people away from buying a legitimate Chrono game in the future.
Anyhow, intellectual property laws themselves are not the issue here. We should all be on notice that Squeenix does not intend to allow the public development of signifiant Chrono series fan projects. That's their prerogative.