I'm surprised by the battering the OP has had on here.
OP, of course it's reasonable to feel annoyed about what has happened. You deserve the courtesy of being told the status of your application. Particularly since you spent seven hours being interviewed/assessed on a trial shift and because they told you that they would let you know by a particular date.
I'd say that your "eagerness to do the job" (a previous poster's advice) has been demonstrated already by the fact that you spent seven hours with them, and have already followed up once by e-mail.
As another poster has pointed out, it's extremely unlikely that one of the HR team or other decision makers has been hit by tragedy. Most likely it's inefficiency, rudeness or a combination of both. A surprising number of people can't bear to deliver bad news, even by e-mail, or think that they are too busy and important to keep candidates informed, or just don't have the social skills to realise that it's nice to be polite.
Job hunting is horrible, and the worst thing about it is the discourtesy of the people you have to deal with, whether HR teams or recruitment consultants. I don't think that it's acceptable to treat candidates like this: not even sending an e-mail to say, "thanks, but we went with somebody else". Nor do I think that it's fair to tell you that you are unreasonable for being annoyed at the treatment you received.
I wouldn't send the e-mail, because it may have repercussions for you in the future. However, I'd call them and ask for an update in a very gentle and polite way. I did this once, after a large company twice, in three years, sent me an e-mail telling me that they would be in touch shortly about an interview for a role they were advertising then never followed up. The second time, I asked the head of recruitment whether they welcomed feedback on the 'candidate experience', and when she said that they did, I described, very politely, how the experience had made me feel and the impression it created of that business. Even though I felt like saying, "you rude, dismissive bastards. I wouldn't want to work for you after this".