IANAL
>If she would likely lose in court [...] I don't see why you would feel sorry for someone in that situation.
A law's existence is not an automatic justification for its invocation. Copyright law is pretty draconian on its own, and automatically-accepted browsewrap/clickwrap Terms of Use generally constrict action even further, making almost anything a breach of contract. Fair use exists, but the standard is fairly high, and it is not really practical for a normal person to get it, especially since each use must be considered in isolation.
Other types of intellectual property would probably also be involved here, including an accusation of "trademark dilution", i.e., harming their mark's value by using it improperly. I haven't seen the C&D but it probably includes various other claims along these lines, all of which she would have to defend, which means big $$$ even if she did win (and if attorney's fees are eventually awarded, they will cover only a tiny fraction of the overall costs).
A large company with giant law firms seeking to punish individual authors for failure to unpublish unflattering blog posts should make you feel sorry, even if those giant law firms are able to contrive a case that shows the conduct was technically illegal. It's not hard to do, especially when there is such a massive resource differential.
In the real world where we're allowed to widen our perspective beyond the legal minutia, this is a blatant attempt to silence press that Zillow doesn't like. The fact that it is possible for big companies to do this to people should seriously frighten everyone.
>doing her a favor by sending a cease and desist instead of going straight to court
A C&D is part of the process. It's not mandatory, but my non-lawyer understanding is that it looks bad to file a suit in this type of case without first asking the defendant to cease and desist (that is, issuing a formal C&D).
Lawyers don't send a C&D to be nice. They do it because the court wants to see that the plaintiff a) sought non-legal remediation before filing a lawsuit and b) because plaintiffs have a responsibility to mitigate ongoing losses when they are able to do so.
The job of the lawyers is to maximize outcomes in favor of their clients, and that means crossing the ts and dotting the is. Failing to send a C&D leaves an opening for the defendant to try to soften your damage claim, pointing out that you did not attempt to mitigate the damage.
If Zillow actually had been damaged by this operation, they would continue the lawsuit after the would-be defendant ceased and desisted and try to recover the damages they suffered. Since this is just a tactic to pressure the other party into unpublishing their content via the legal strongarm, money won't be wasted on a lawsuit after the publisher has been bullied into submission.
IANAL