Babysitter no-show: leave bad review or let it go?

Yes. That is not OK behavior and I wouldn't want to hire someone like that. You're not screwing her over. She screwed herself over by making a really, really bad impression by not even letting you know she couldn't show up.

I would DEFINITELY leave the review. Be factual and neutral in tone, pretty much just reporting what you've just told us (but leaving out any assumptions you're making as to the reason for her no-show). If this person wants to make a real go of being a professional babysitter, she needs to know that honoring her time commitments is a huge part of her responsibilities and that failing to do so will have consequences. Moreover, surely other fellow customers would appreciate knowing this so that at the very least, they can give her a trial run at some non-critical time themselves.

There are plenty of good reasons why she might not have shown up. There are very few good reasons for why she didn't follow up proactively or respond to your messages or phone calls.

You have no professional relationship with this woman and no basis to judge her competence as a child care provider. You have no understanding of what happened and cannot even confirm that she personally understood the details of your appointment or that she personally has received your messages. Move on and let people who have an actual professional relationship with her evaluate her performance.

I think sending the followup messages on the site, to which she apparently didn't reply, was probably chance enough to explain herself again.

failed to show up to her (paid) trial, and did not respond to voicemails or messages following up. Just add "it's now x days later and we have not heard from them", and you've got a factual and useful review. Do you think she tried but was unable to show up but to embarrassed to let you know what was going on? That's not quite as bad as a full-on no show. I'm not sure how one would tell the difference between a full-on no show and a no-show where the person had some reason for not showing up that they never told you about. However, writing a fact based review stating only your own experiences will avoid anything about why the person did not show up or contact you -- readers can draw their own conclusions about how bad that is.

People are considering leaving their children in her care. Leaving a review with the facts of the missed trial is 100% appropriate.

Follow the "A Small Good Thing" Rule: don't act until you hear from her or someone close to her regarding what happened. It's the decent thing to do. If you do NOT receive a damned good, ironclad excuse, however, absolutely leave a bad review.

Every website that allows users to leave reviews has a mechanism to modify, follow up, or at least remove a review after the fact. I would absolutely state the facts of what happened in the form of a review. If the caregiver contacts you afterward with an ironclad excuse that makes you wish you hadn't left the review, it can be removed then.